Chaos, Solitons and Fractals, ISSN 0960-0779, 2009, Volume 42, Issue 3, pp. 1356 - 1363

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method...

PHYSICS, MULTIDISCIPLINARY | DAVEY-STEWARTSON EQUATION | MAPPING METHOD | F-EXPANSION METHOD | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOLITARY-WAVE SOLUTIONS | EXP-FUNCTION METHOD | WRONSKIAN SOLUTIONS | NONLINEAR EVOLUTION-EQUATIONS | GENERALIZED KDV EQUATION | TANH-FUNCTION METHOD

PHYSICS, MULTIDISCIPLINARY | DAVEY-STEWARTSON EQUATION | MAPPING METHOD | F-EXPANSION METHOD | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOLITARY-WAVE SOLUTIONS | EXP-FUNCTION METHOD | WRONSKIAN SOLUTIONS | NONLINEAR EVOLUTION-EQUATIONS | GENERALIZED KDV EQUATION | TANH-FUNCTION METHOD

Journal Article

AIP Advances, ISSN 2158-3226, 03/2013, Volume 3, Issue 3, pp. 32116 - 032116

In this article, new (G′/G)-expansion method and new generalized (G′/G)-expansion method is proposed to generate more general and abundant new exact traveling...

F-EXPANSION | PHYSICS, APPLIED | SOLITONS | MATERIALS SCIENCE, MULTIDISCIPLINARY | EXP-FUNCTION METHOD | NANOSCIENCE & NANOTECHNOLOGY | PERIODIC-WAVE SOLUTIONS | Nonlinear evolution equations | Traveling waves | Nonlinearity | Consumer goods | Real time | Mathematical analysis

F-EXPANSION | PHYSICS, APPLIED | SOLITONS | MATERIALS SCIENCE, MULTIDISCIPLINARY | EXP-FUNCTION METHOD | NANOSCIENCE & NANOTECHNOLOGY | PERIODIC-WAVE SOLUTIONS | Nonlinear evolution equations | Traveling waves | Nonlinearity | Consumer goods | Real time | Mathematical analysis

Journal Article

Ain Shams Engineering Journal, ISSN 2090-4479, 03/2014, Volume 5, Issue 1, pp. 247 - 256

The modified simple equation (MSE) method is promising for finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical...

(2 + 1)-Dimensional Zoomeron equation | Solitary wave solutions | The (2 + 1)-dimensional Burgers equation | Modified simple equation method | Traveling wave solutions | Exp-function method | The (2 + 1)-dimensional Burgers equation | (2 + 1)-Dimensional Zoomeron equation

(2 + 1)-Dimensional Zoomeron equation | Solitary wave solutions | The (2 + 1)-dimensional Burgers equation | Modified simple equation method | Traveling wave solutions | Exp-function method | The (2 + 1)-dimensional Burgers equation | (2 + 1)-Dimensional Zoomeron equation

Journal Article

4.
Full Text
A generalized ( G ′ G ) -expansion method for the mKdV equation with variable coefficients

Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 13, pp. 2254 - 2257

In this Letter, a generalized -expansion method is proposed to seek exact solutions of nonlinear evolution equations. Being concise and straightforward, this...

Nonlinear evolution equations | Generalized [formula omitted]-expansion method | Trigonometric function solution | Hyperbolic function solution | Rational solution | Generalized (frac(G | G))-expansion method | PHYSICS, MULTIDISCIPLINARY | ELLIPTIC FUNCTION EXPANSION | KADOMSTEV-PETVIASHVILI EQUATION | hyperbolic function solution | F-EXPANSION METHOD | generalized (G '/G)-expansion method | HOMOTOPY PERTURBATION METHOD | BROER-KAUP EQUATIONS | VARIATIONAL ITERATION METHOD | TRAVELING-WAVE SOLUTIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | EXP-FUNCTION METHOD | trigonometric function solution | rational solution | nonlinear evolution equations | NONLINEAR EVOLUTION-EQUATIONS

Nonlinear evolution equations | Generalized [formula omitted]-expansion method | Trigonometric function solution | Hyperbolic function solution | Rational solution | Generalized (frac(G | G))-expansion method | PHYSICS, MULTIDISCIPLINARY | ELLIPTIC FUNCTION EXPANSION | KADOMSTEV-PETVIASHVILI EQUATION | hyperbolic function solution | F-EXPANSION METHOD | generalized (G '/G)-expansion method | HOMOTOPY PERTURBATION METHOD | BROER-KAUP EQUATIONS | VARIATIONAL ITERATION METHOD | TRAVELING-WAVE SOLUTIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | EXP-FUNCTION METHOD | trigonometric function solution | rational solution | nonlinear evolution equations | NONLINEAR EVOLUTION-EQUATIONS

Journal Article

Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 19, pp. 3400 - 3406

In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave...

Modified Zakharov–Kuznetsov equation | Konopelchenko–Dubrovsky equation | [formula omitted]-expansion method | Boussinesq equation | Konopelchenko-Dubrovsky equation | Modified Zakharov-Kuznetsov equation | G))-expansion method | frac(G | modified zakharov-kuznetsov equation | (G'/G)-expansion method | TRAVELING-WAVE SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | EXP-FUNCTION METHOD | boussinesq equation | EXTENDED TANH METHOD | konopelchenko-dubrovsky equation

Modified Zakharov–Kuznetsov equation | Konopelchenko–Dubrovsky equation | [formula omitted]-expansion method | Boussinesq equation | Konopelchenko-Dubrovsky equation | Modified Zakharov-Kuznetsov equation | G))-expansion method | frac(G | modified zakharov-kuznetsov equation | (G'/G)-expansion method | TRAVELING-WAVE SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | EXP-FUNCTION METHOD | boussinesq equation | EXTENDED TANH METHOD | konopelchenko-dubrovsky equation

Journal Article

Zeitschrift für Naturforschung A, ISSN 0932-0784, 02/2016, Volume 71, Issue 2, pp. 103 - 112

The modified simple equation method, the exp-function method, and the method of soliton ansatz for solving nonlinear partial differential equations are...

Method of Soliton Ansatz | 02.30.Ik | Exp-Function Method | Solitary Solutions | 05.45.Yv | Bright–Dark Soliton Solutions | Exact Solutions | 02.30.Jr | Modified Simple Equation Method | Long–Short Wave Resonance Equations | Long-Short Wave Resonance Equations | Bright-Dark Soliton Solutions | PERIODIC-SOLUTIONS | SYMMETRY METHOD | PHYSICS, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | POWER-LAW NONLINEARITY | NONLINEAR EVOLUTION-EQUATIONS | TANH-FUNCTION METHOD | MEW | Wave equation | Usage | Resonance | Differential equations, Partial | Analysis | Solitons

Method of Soliton Ansatz | 02.30.Ik | Exp-Function Method | Solitary Solutions | 05.45.Yv | Bright–Dark Soliton Solutions | Exact Solutions | 02.30.Jr | Modified Simple Equation Method | Long–Short Wave Resonance Equations | Long-Short Wave Resonance Equations | Bright-Dark Soliton Solutions | PERIODIC-SOLUTIONS | SYMMETRY METHOD | PHYSICS, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | POWER-LAW NONLINEARITY | NONLINEAR EVOLUTION-EQUATIONS | TANH-FUNCTION METHOD | MEW | Wave equation | Usage | Resonance | Differential equations, Partial | Analysis | Solitons

Journal Article

Optical and Quantum Electronics, ISSN 0306-8919, 3/2018, Volume 50, Issue 3, pp. 1 - 20

In this study, some new traveling wave solutions for fractional partial differential equations (PDEs) have been developed. The time-fractional Burgers...

Burgers equations | Fractional modified Reimann-Liouville derivative | ( $$\frac{G^{'}}{G^{2}}$$ G ′ G 2 )-Expansion method | Whitham Broer Kuap equations | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Computer Communication Networks | Physics | Traveling wave solution | Electrical Engineering | Biological population model | (G′G2)-Expansion method | QUANTUM SCIENCE & TECHNOLOGY | 1ST INTEGRAL METHOD | EXP-FUNCTION METHOD | FUNCTIONAL VARIABLE METHOD | OPTICS | (G '/G)-Expansion method | ENGINEERING, ELECTRICAL & ELECTRONIC | Water waves | Mortality | Methods | Differential equations | Fluid mechanics | Nonlinear equations | Wave propagation | Partial differential equations | Computational fluid dynamics | Mathematical models | Burgers equation | Shallow water

Burgers equations | Fractional modified Reimann-Liouville derivative | ( $$\frac{G^{'}}{G^{2}}$$ G ′ G 2 )-Expansion method | Whitham Broer Kuap equations | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Computer Communication Networks | Physics | Traveling wave solution | Electrical Engineering | Biological population model | (G′G2)-Expansion method | QUANTUM SCIENCE & TECHNOLOGY | 1ST INTEGRAL METHOD | EXP-FUNCTION METHOD | FUNCTIONAL VARIABLE METHOD | OPTICS | (G '/G)-Expansion method | ENGINEERING, ELECTRICAL & ELECTRONIC | Water waves | Mortality | Methods | Differential equations | Fluid mechanics | Nonlinear equations | Wave propagation | Partial differential equations | Computational fluid dynamics | Mathematical models | Burgers equation | Shallow water

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 08/2008, Volume 202, Issue 1, pp. 275 - 286

The generalized short wave equation (GSWW) is studied by three distinct methods. The Hirota's bilinear method is used to derive multiple-soliton solutions for...

Multiple-soliton solutions | Generalized shallow water wave equation | tanh-coth method | Exp-function method | Hirota bilinear method | MATHEMATICS, APPLIED | generalized shallow water wave equation | SEARCH | multiple-soliton solutions | 3-SOLITON CONDITION | NONLINEAR EVOLUTION | SOLITONS | BILINEAR EQUATIONS | MULTIPLE-FRONT SOLUTIONS | MODEL-EQUATIONS

Multiple-soliton solutions | Generalized shallow water wave equation | tanh-coth method | Exp-function method | Hirota bilinear method | MATHEMATICS, APPLIED | generalized shallow water wave equation | SEARCH | multiple-soliton solutions | 3-SOLITON CONDITION | NONLINEAR EVOLUTION | SOLITONS | BILINEAR EQUATIONS | MULTIPLE-FRONT SOLUTIONS | MODEL-EQUATIONS

Journal Article

Optik, ISSN 0030-4026, 10/2016, Volume 127, Issue 20, pp. 9603 - 9620

In this paper, by introducing new approach, the improved tan( ( )/2)-expansion method (ITEM) is further extended into Gerdjikov–Ivanov (GI) model. As a result,...

Periodic and rational solutions | Kink | Improved tan(ϕ(ξ)/2)-expansion method | Gerdjikov–Ivanov model | Solitons | Gerdjikov-ivanov model | DARBOUX TRANSFORMATION | ENVELOPE SOLITONS | BISWAS-MILOVIC EQUATION | EVOLUTION-EQUATIONS | WAVE SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | Improved tan(phi(xi)/2)-expansion method | PARTIAL-DIFFERENTIAL-EQUATIONS | KERR LAW NONLINEARITY | EXP-FUNCTION METHOD | MADELUNGS FLUID | OPTICS

Periodic and rational solutions | Kink | Improved tan(ϕ(ξ)/2)-expansion method | Gerdjikov–Ivanov model | Solitons | Gerdjikov-ivanov model | DARBOUX TRANSFORMATION | ENVELOPE SOLITONS | BISWAS-MILOVIC EQUATION | EVOLUTION-EQUATIONS | WAVE SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | Improved tan(phi(xi)/2)-expansion method | PARTIAL-DIFFERENTIAL-EQUATIONS | KERR LAW NONLINEARITY | EXP-FUNCTION METHOD | MADELUNGS FLUID | OPTICS

Journal Article

Physics Letters A, ISSN 0375-9601, 2009, Volume 373, Issue 10, pp. 905 - 910

In this Letter, an algorithm is devised for using the -expansion method to solve nonlinear differential-difference equations. With the aid of symbolic...

Nonlinear differential-difference equations | Hyperbolic function solutions | [formula omitted]-expansion method | Trigonometric function solutions | G))-expansion method | frac(G | PHYSICS, MULTIDISCIPLINARY | ELLIPTIC FUNCTION EXPANSION | KADOMSTEV-PETVIASHVILI EQUATION | F-EXPANSION METHOD | EVOLUTION-EQUATIONS | HOMOTOPY PERTURBATION METHOD | BROER-KAUP EQUATIONS | (G '/G)-expansion method | VARIATIONAL ITERATION METHOD | TRAVELING-WAVE SOLUTIONS | VARIABLE-COEFFICIENTS | EXP-FUNCTION METHOD | Algorithms | Universities and colleges | Analysis | Methods

Nonlinear differential-difference equations | Hyperbolic function solutions | [formula omitted]-expansion method | Trigonometric function solutions | G))-expansion method | frac(G | PHYSICS, MULTIDISCIPLINARY | ELLIPTIC FUNCTION EXPANSION | KADOMSTEV-PETVIASHVILI EQUATION | F-EXPANSION METHOD | EVOLUTION-EQUATIONS | HOMOTOPY PERTURBATION METHOD | BROER-KAUP EQUATIONS | (G '/G)-expansion method | VARIATIONAL ITERATION METHOD | TRAVELING-WAVE SOLUTIONS | VARIABLE-COEFFICIENTS | EXP-FUNCTION METHOD | Algorithms | Universities and colleges | Analysis | Methods

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 2012, Volume 17, Issue 6, pp. 2248 - 2253

► Modification of the one of old method for finding exact solutions of nonlinear differential equations is considered. ► Examples of application of method are...

Nonlinear evolution equation | Fisher equation | Nonlinear differential equation of the seven order | Traveling wave solution | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | SIMPLEST EQUATION | EVOLUTION-EQUATIONS | PHYSICS, MATHEMATICAL | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EXP-FUNCTION METHOD | KDV | Methods | Differential equations | Nonlinearity | Mathematical models | Computer simulation | Mathematical analysis | Exact solutions

Nonlinear evolution equation | Fisher equation | Nonlinear differential equation of the seven order | Traveling wave solution | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | SIMPLEST EQUATION | EVOLUTION-EQUATIONS | PHYSICS, MATHEMATICAL | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EXP-FUNCTION METHOD | KDV | Methods | Differential equations | Nonlinearity | Mathematical models | Computer simulation | Mathematical analysis | Exact solutions

Journal Article

Mathematical Problems in Engineering, ISSN 1024-123X, 2010, Volume 2010, pp. 1 - 19

We construct the traveling wave solutions of the (1+1)-dimensional modified Benjamin-Bona-Mahony equation, the (2+1)-dimensional typical breaking soliton...

TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | BREAKING SOLITON EQUATION | EXP-FUNCTION METHOD | EVOLUTION-EQUATIONS | DIFFERENTIAL-DIFFERENCE EQUATIONS | Mathematical models | Algebra | Derivatives | Partial differential equations | Boussinesq equations | Mathematical analysis | Rational functions | Exact solutions | Solitons | Differential equations | Nonlinearity | Hyperbolic functions | Solitary waves

TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | BREAKING SOLITON EQUATION | EXP-FUNCTION METHOD | EVOLUTION-EQUATIONS | DIFFERENTIAL-DIFFERENCE EQUATIONS | Mathematical models | Algebra | Derivatives | Partial differential equations | Boussinesq equations | Mathematical analysis | Rational functions | Exact solutions | Solitons | Differential equations | Nonlinearity | Hyperbolic functions | Solitary waves

Journal Article

Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 47, pp. 7011 - 7015

In this Letter, the Exp-function method, with the aid of a symbolic computation system such as , is applied to the ( )-dimensional Jimbo–Miwa equation to show...

( [formula omitted])-dimensional Jimbo–Miwa equation | Generalized solitary solutions | Exp-function method | (3 + 1)-dimensional Jimbo-Miwa equation | EXPANSION METHOD | PERIODIC-SOLUTIONS | LATTICE EQUATION | PHYSICS, MULTIDISCIPLINARY | SYMMETRY ALGEBRA | HOMOTOPY PERTURBATION METHOD | WAVE EQUATIONS | VARIABLE-COEFFICIENTS | SOLITON-SOLUTIONS | (3+1)-dimensional Jimbo-Miwa equation | KDV EQUATION | NONLINEAR EVOLUTION-EQUATIONS

( [formula omitted])-dimensional Jimbo–Miwa equation | Generalized solitary solutions | Exp-function method | (3 + 1)-dimensional Jimbo-Miwa equation | EXPANSION METHOD | PERIODIC-SOLUTIONS | LATTICE EQUATION | PHYSICS, MULTIDISCIPLINARY | SYMMETRY ALGEBRA | HOMOTOPY PERTURBATION METHOD | WAVE EQUATIONS | VARIABLE-COEFFICIENTS | SOLITON-SOLUTIONS | (3+1)-dimensional Jimbo-Miwa equation | KDV EQUATION | NONLINEAR EVOLUTION-EQUATIONS

Journal Article

Journal of Applied Mathematics, ISSN 1110-757X, 2012, Volume 2012, pp. 1 - 8

The two variables (G'/G, 1/G)-expansion method is proposed in this paper to construct new exact traveling wave solutions with parameters of the nonlinear (3 +...

EXPANSION METHOD | (G'/G)-EXPANSION METHOD | MATHEMATICS, APPLIED | EXP-FUNCTION METHOD | DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | ELLIPTIC FUNCTION SOLUTIONS | Research | Variables (Mathematics) | Differential equations, Partial | Wave-motion, Theory of | Studies | Variables | Algorithms | Algebra | Ordinary differential equations | Derivatives | Expansion

EXPANSION METHOD | (G'/G)-EXPANSION METHOD | MATHEMATICS, APPLIED | EXP-FUNCTION METHOD | DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | ELLIPTIC FUNCTION SOLUTIONS | Research | Variables (Mathematics) | Differential equations, Partial | Wave-motion, Theory of | Studies | Variables | Algorithms | Algebra | Ordinary differential equations | Derivatives | Expansion

Journal Article

Mathematical Problems in Engineering, ISSN 1024-123X, 2014, Volume 2014, pp. 1 - 20

The two variable (G'/G, 1/G)-expansion method is employed to construct exact traveling wave solutions with parameters of two higher order nonlinear evolution...

EXPANSION METHOD | (G'/G)-EXPANSION METHOD | PERIODIC-SOLUTIONS | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOLITONS | ENGINEERING, MULTIDISCIPLINARY | SINE-COSINE METHODS | EXP-FUNCTION METHOD | ELLIPTIC FUNCTION SOLUTIONS | SOLITARY-WAVE | TANH-FUNCTION-METHOD | Research | Differential equations, Nonlinear | Variables (Mathematics) | Differential equations, Partial | Mathematical research | Expansion | Quantum field theory | Partial differential equations | Mathematical analysis | Klein-Gordon equation | Nonlinear evolution equations | Tools | Traveling waves | Nonlinearity | Solitary waves

EXPANSION METHOD | (G'/G)-EXPANSION METHOD | PERIODIC-SOLUTIONS | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOLITONS | ENGINEERING, MULTIDISCIPLINARY | SINE-COSINE METHODS | EXP-FUNCTION METHOD | ELLIPTIC FUNCTION SOLUTIONS | SOLITARY-WAVE | TANH-FUNCTION-METHOD | Research | Differential equations, Nonlinear | Variables (Mathematics) | Differential equations, Partial | Mathematical research | Expansion | Quantum field theory | Partial differential equations | Mathematical analysis | Klein-Gordon equation | Nonlinear evolution equations | Tools | Traveling waves | Nonlinearity | Solitary waves

Journal Article

PLoS ONE, ISSN 1932-6203, 05/2013, Volume 8, Issue 5, pp. e64618 - e64618

The generalized and improved (G'/G)-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of...

EXPANSION METHOD | F-EXPANSION | TANH-COTH METHOD | SOLITONS | MULTIDISCIPLINARY SCIENCES | EXP-FUNCTION METHOD | SOLITARY WAVE SOLUTIONS | DIFFERENTIAL-EQUATIONS | ELLIPTIC FUNCTION SOLUTIONS | NONLINEAR EVOLUTION-EQUATIONS | Computer Graphics | Software | Algorithms | Nonlinear Dynamics | Computer Simulation | Analysis | Methods | Differential equations | Nonlinear equations | Partial differential equations | Nonlinear differential equations | Hyperbolic functions | Physics | Studies | Mathematical problems | Engineering | Algebra | Applied mathematics | Rational functions | Nonlinear evolution equations | Ordinary differential equations | Polynomials | Mathematical models | Informatics | Index Medicus

EXPANSION METHOD | F-EXPANSION | TANH-COTH METHOD | SOLITONS | MULTIDISCIPLINARY SCIENCES | EXP-FUNCTION METHOD | SOLITARY WAVE SOLUTIONS | DIFFERENTIAL-EQUATIONS | ELLIPTIC FUNCTION SOLUTIONS | NONLINEAR EVOLUTION-EQUATIONS | Computer Graphics | Software | Algorithms | Nonlinear Dynamics | Computer Simulation | Analysis | Methods | Differential equations | Nonlinear equations | Partial differential equations | Nonlinear differential equations | Hyperbolic functions | Physics | Studies | Mathematical problems | Engineering | Algebra | Applied mathematics | Rational functions | Nonlinear evolution equations | Ordinary differential equations | Polynomials | Mathematical models | Informatics | Index Medicus

Journal Article

Journal of Applied Mathematics, ISSN 1110-757X, 2014, Volume 2014, pp. 1 - 6

New exact traveling wave solutions of a higher-order KdV equation type are studied by the (G'/G)-expansion method, where G = G (xi) satisfies a second-order...

EXPANSION METHOD | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | NONLINEAR EVOLUTION-EQUATIONS | EXP-FUNCTION METHOD | Differential equations, Linear | Functions | Research | Functional equations | Mathematical research | Studies | Ordinary differential equations | Nonlinear programming | Expansion | Traveling waves | Hyperbolic functions | Trigonometric functions | Mathematical analysis | Rational functions | Differential equations

EXPANSION METHOD | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | NONLINEAR EVOLUTION-EQUATIONS | EXP-FUNCTION METHOD | Differential equations, Linear | Functions | Research | Functional equations | Mathematical research | Studies | Ordinary differential equations | Nonlinear programming | Expansion | Traveling waves | Hyperbolic functions | Trigonometric functions | Mathematical analysis | Rational functions | Differential equations

Journal Article

18.
Full Text
The two-variable (G′/G,1/G)-expansion method for solving the nonlinear KdV-mKdV equation

Mathematical Problems in Engineering, ISSN 1024-123X, 2012, Volume 2012, pp. 1 - 14

We apply the two-variable (G'/G, 1/G)-expansion method to construct new exact traveling wave solutions with parameters of the nonlinear (1 + 1)-dimensional...

EXPANSION METHOD | (G'/G)-EXPANSION METHOD | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | EXP-FUNCTION METHOD | DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | ELLIPTIC FUNCTION SOLUTIONS | Studies | Algorithms | Algebra | Ordinary differential equations | Derivatives | Expansion | Quantum field theory | Construction | Mathematical analysis | Nonlinear evolution equations | Tools | Traveling waves | Nonlinearity | Solitary waves

EXPANSION METHOD | (G'/G)-EXPANSION METHOD | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | EXP-FUNCTION METHOD | DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | ELLIPTIC FUNCTION SOLUTIONS | Studies | Algorithms | Algebra | Ordinary differential equations | Derivatives | Expansion | Quantum field theory | Construction | Mathematical analysis | Nonlinear evolution equations | Tools | Traveling waves | Nonlinearity | Solitary waves

Journal Article

Mathematical Problems in Engineering, ISSN 1024-123X, 2014, Volume 2014, pp. 1 - 10

The two-variable (G'/G, 1/G)-expansion method is employed to construct exact traveling wave solutions with parameters of nanobiosciences partial differential...

(G'/G)-EXPANSION METHOD | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | HEAT-TRANSFER | EXP-FUNCTION METHOD | FUNCTION EXPANSION METHOD | EVOLUTION-EQUATIONS | ELLIPTIC FUNCTION SOLUTIONS | TANH-FUNCTION-METHOD | FLOW | Usage | Differential equations, Partial | Analysis | Mathematical physics | Solitons | Ordinary differential equations | Derivatives | Partial differential equations | Expansion | Mathematical analysis | Exact solutions | Tools | Traveling waves | Nonlinearity | Nanostructure | Solitary waves

(G'/G)-EXPANSION METHOD | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | HEAT-TRANSFER | EXP-FUNCTION METHOD | FUNCTION EXPANSION METHOD | EVOLUTION-EQUATIONS | ELLIPTIC FUNCTION SOLUTIONS | TANH-FUNCTION-METHOD | FLOW | Usage | Differential equations, Partial | Analysis | Mathematical physics | Solitons | Ordinary differential equations | Derivatives | Partial differential equations | Expansion | Mathematical analysis | Exact solutions | Tools | Traveling waves | Nonlinearity | Nanostructure | Solitary waves

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2009, Volume 211, Issue 2, pp. 531 - 536

In this study, we demonstrate the validity and reliability of the so-called ( / )-expansion method via symbolic computation. For illustrative examples, we...

Ninth-order KdV equation | ( [formula omitted]/ G)-expansion method | Solitary wave solutions | Sixth-order Boussinesq equation | Traveling wave solutions | G)-expansion method | (G '/G)-expansion method | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | EXP-FUNCTION METHOD | EVOLUTION-EQUATIONS

Ninth-order KdV equation | ( [formula omitted]/ G)-expansion method | Solitary wave solutions | Sixth-order Boussinesq equation | Traveling wave solutions | G)-expansion method | (G '/G)-expansion method | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | EXP-FUNCTION METHOD | EVOLUTION-EQUATIONS

Journal Article