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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 ( G ′ G ) -expansion method is proposed to seek exact solutions of nonlinear evolution equations. Being concise and...

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

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 07/2017, Volume 140, pp. 467 - 468

This manuscript presents a short note on the “Exact solutions of the unstable nonlinear Schrödinger equation with the new Jacobi elliptic function rational...

Unstable nonlinear Schrödinger equation | New Jacobi elliptic function rational expansion method | Unstable nonlinear Schrodinger equation | OPTICS

Unstable nonlinear Schrödinger equation | New Jacobi elliptic function rational expansion method | Unstable nonlinear Schrodinger equation | OPTICS

Journal Article

Optical and Quantum Electronics, ISSN 0306-8919, 4/2016, Volume 48, Issue 4, pp. 1 - 8

We generalize the Jacobi elliptic function expansion method used to solve the (3 + 1)-dimensional nonlinear Schrödinger equation for the case of an arbitrary...

Optics, Optoelectronics, Plasmonics and Optical Devices | Jacobi elliptic functions | Characterization and Evaluation of Materials | F-expansion | Nonlinear Schrödinger equation | Computer Communication Networks | Physics | Electrical Engineering | INTEGRALS | TRAVELING-WAVE SOLUTIONS | EVOLUTION | KERR LAW NONLINEARITY | Nonlinear Schrodinger equation | KIND | OPTICS | ENGINEERING, ELECTRICAL & ELECTRONIC

Optics, Optoelectronics, Plasmonics and Optical Devices | Jacobi elliptic functions | Characterization and Evaluation of Materials | F-expansion | Nonlinear Schrödinger equation | Computer Communication Networks | Physics | Electrical Engineering | INTEGRALS | TRAVELING-WAVE SOLUTIONS | EVOLUTION | KERR LAW NONLINEARITY | Nonlinear Schrodinger equation | KIND | OPTICS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 12/2016, Volume 127, Issue 23, pp. 11124 - 11130

In this paper, by using the new Jacobi elliptic function rational expansion method and the exponential rational function method, new exact solutions of the...

Exponential rational function method | Exact solutions | Unstable nonlinear Schrödinger equation | New Jacobi elliptic function rational expansion method | Unstable nonlinear Schrodinger equation | OPTICS

Exponential rational function method | Exact solutions | Unstable nonlinear Schrödinger equation | New Jacobi elliptic function rational expansion method | Unstable nonlinear Schrodinger equation | OPTICS

Journal Article

Optik, ISSN 0030-4026, 04/2019, Volume 183, pp. 571 - 578

The extended Jacobi's elliptic function scheme is implemented to retrieve bright, dark and singular highly dispersive optical solitons that is studied in...

Cubic–quintic–septic law | Jacobi's elliptic function | Highly dispersive solitons | Cubic-quintic-septic law | OPTICS

Cubic–quintic–septic law | Jacobi's elliptic function | Highly dispersive solitons | Cubic-quintic-septic law | 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 ( G ′ G ) -expansion method to solve nonlinear differential-difference equations. With the aid of...

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

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 4/2018, Volume 2018, Issue 4, pp. 1 - 31

We propose a set of novel expansions of Nekrasov’s instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group...

Solitons Monopoles and Instantons | Supersymmetric Gauge Theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | VERTEX | N=2 GAUGE-THEORIES | DUALITY | ELLIPTIC GENERA | PHYSICS, PARTICLES & FIELDS | Supersymmetry | Partitions | Correlators | Subspaces | Yang-Mills theory | Mathematics - Quantum Algebra | Subatomic Physics | High Energy Physics | Theory | Nuclear and particle physics. Atomic energy. Radioactivity | Subatomär fysik | High Energy Physics - Theory | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences

Solitons Monopoles and Instantons | Supersymmetric Gauge Theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | VERTEX | N=2 GAUGE-THEORIES | DUALITY | ELLIPTIC GENERA | PHYSICS, PARTICLES & FIELDS | Supersymmetry | Partitions | Correlators | Subspaces | Yang-Mills theory | Mathematics - Quantum Algebra | Subatomic Physics | High Energy Physics | Theory | Nuclear and particle physics. Atomic energy. Radioactivity | Subatomär fysik | High Energy Physics - Theory | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences

Journal Article

Physics Letters A, ISSN 0375-9601, 2001, Volume 289, Issue 1, pp. 69 - 74

A Jacobi elliptic function expansion method, which is more general than the hyperbolic tangent function expansion method, is proposed to construct the exact...

Jacobi elliptic function | Nonlinear equation | Cnoidal wave solution | PHYSICS, MULTIDISCIPLINARY | cnoidal wave solution | nonlinear equation

Jacobi elliptic function | Nonlinear equation | Cnoidal wave solution | PHYSICS, MULTIDISCIPLINARY | cnoidal wave solution | nonlinear equation

Journal Article

PLoS ONE, ISSN 1932-6203, 05/2013, Volume 8, Issue 5, p. 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 | SOLITARY WAVE SOLUTIONS | F-EXPANSION | ELLIPTIC FUNCTION SOLUTIONS | MULTIDISCIPLINARY SCIENCES | EXP-FUNCTION METHOD | 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

EXPANSION METHOD | SOLITARY WAVE SOLUTIONS | F-EXPANSION | ELLIPTIC FUNCTION SOLUTIONS | MULTIDISCIPLINARY SCIENCES | EXP-FUNCTION METHOD | 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

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2011, Volume 235, Issue 14, pp. 4117 - 4127

In this work, a new generalized Jacobi elliptic function rational expansion method is based upon twenty-four Jacobi elliptic functions and eight double...

(3+1)-dimensional Kadmtsev–Petviashvili equation | New generalized Jacobi elliptic function expansion method | Solitary wave solutions | (3+1)-dimensional Kadmtsev-Petviashvili equation | SOLITON-LIKE SOLUTIONS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | SIMILARITY SOLUTIONS | (2+1)-DIMENSIONAL BOUSSINESQ EQUATION | NONLINEAR-WAVE EQUATIONS | KADOMTSEV-PETVIASHVILI EQUATION | ISOVECTOR FIELDS | GORDON EQUATION | EXP-FUNCTION METHOD | TANH-FUNCTION METHOD | Mathematical models | Elliptic functions | Partial differential equations | Computation | Mathematical analysis | Nonlinear differential equations

(3+1)-dimensional Kadmtsev–Petviashvili equation | New generalized Jacobi elliptic function expansion method | Solitary wave solutions | (3+1)-dimensional Kadmtsev-Petviashvili equation | SOLITON-LIKE SOLUTIONS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | SIMILARITY SOLUTIONS | (2+1)-DIMENSIONAL BOUSSINESQ EQUATION | NONLINEAR-WAVE EQUATIONS | KADOMTSEV-PETVIASHVILI EQUATION | ISOVECTOR FIELDS | GORDON EQUATION | EXP-FUNCTION METHOD | TANH-FUNCTION METHOD | Mathematical models | Elliptic functions | Partial differential equations | Computation | Mathematical analysis | Nonlinear differential equations

Journal Article

Optik, ISSN 0030-4026, 04/2019, Volume 183, pp. 395 - 400

This paper utilizes Jacobi's elliptic function expansion to obtain highly dispersive dark, singular, and their combinations thereof, optical solitons. The...

Kerr law | Jacobi's elliptic function | Dispersive solitons | WAVE SOLUTIONS | OPTICS

Kerr law | Jacobi's elliptic function | Dispersive solitons | WAVE SOLUTIONS | OPTICS

Journal Article

Optics Communications, ISSN 0030-4018, 08/2015, Volume 349, pp. 185 - 192

Elliptic Cylindrical Waves (ECW), defined as the product of an angular Mathieu function by its corresponding radial Mathieu function, occur in the solution of...

Plane surface | Plane-wave spectrum | Fourier integral | Mathieu functions | Elliptic cylinder | CIRCULAR-CYLINDER | SPHERE | SURFACE | LOSSY MEDIA | OPTICS | SCATTERING

Plane surface | Plane-wave spectrum | Fourier integral | Mathieu functions | Elliptic cylinder | CIRCULAR-CYLINDER | SPHERE | SURFACE | LOSSY MEDIA | OPTICS | SCATTERING

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, 2011, Volume 218, Issue 4, pp. 1308 - 1316

In this paper, a variable-coefficient Jacobi elliptic function expansion method is proposed to seek more general exact solutions of nonlinear partial...

Jacobi elliptic function solutions | Non-travelling wave and coefficient function solutions | Variable-coefficient Jacobi elliptic function expansion method | Trigonometric function solutions | Soliton-like solutions | MATHEMATICS, APPLIED | SERIES | KADOMSTEV-PETVIASHVILI EQUATION | PERIODIC-WAVE SOLUTIONS | TANH-FUNCTION | PARTIAL-DIFFERENTIAL-EQUATIONS | FAMILIES | SYMBOLIC COMPUTATION | BOUSSINESQ EQUATIONS | NONLINEAR EVOLUTION-EQUATIONS | Partial differential equations | Computation | Mathematical analysis | Nonlinear differential equations | Exact solutions | Mathematical models | Elliptic functions | Trigonometric functions

Jacobi elliptic function solutions | Non-travelling wave and coefficient function solutions | Variable-coefficient Jacobi elliptic function expansion method | Trigonometric function solutions | Soliton-like solutions | MATHEMATICS, APPLIED | SERIES | KADOMSTEV-PETVIASHVILI EQUATION | PERIODIC-WAVE SOLUTIONS | TANH-FUNCTION | PARTIAL-DIFFERENTIAL-EQUATIONS | FAMILIES | SYMBOLIC COMPUTATION | BOUSSINESQ EQUATIONS | NONLINEAR EVOLUTION-EQUATIONS | Partial differential equations | Computation | Mathematical analysis | Nonlinear differential equations | Exact solutions | Mathematical models | Elliptic functions | Trigonometric functions

Journal Article

Physics Letters A, ISSN 0375-9601, 2001, Volume 290, Issue 1, pp. 72 - 76

New Jacobi elliptic functions are applied in Jacobi elliptic function expansion method to construct the exact periodic solutions of nonlinear wave equations....

Jacobi elliptic function | Nonlinear equation | Periodic wave solution | periodic wave solution | PHYSICS, MULTIDISCIPLINARY | nonlinear equation

Jacobi elliptic function | Nonlinear equation | Periodic wave solution | periodic wave solution | PHYSICS, MULTIDISCIPLINARY | nonlinear equation

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 2007, Volume 12, Issue 5, pp. 627 - 635

In this letter, an extended Jacobi elliptic function expansion method is proposed for constructing the exact solutions of nonlinear wave equations. The...

Jacobi elliptic functions | Jacobi elliptic function expansion method | Solitary wave solutions | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL

Jacobi elliptic functions | Jacobi elliptic function expansion method | Solitary wave solutions | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2019, Volume 479, Issue 1, pp. 90 - 121

Motivated by our previous work on hypergeometric functions and the parbelos constant, we perform a deeper investigation on the interplay among generalized...

Fourier–Legendre theory | Complete elliptic integral | Hypergeometric series | Harmonic number | Infinite series | Fourier-Legendre theory | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | SERIES | IDENTITIES | Rypergeometric series

Fourier–Legendre theory | Complete elliptic integral | Hypergeometric series | Harmonic number | Infinite series | Fourier-Legendre theory | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | SERIES | IDENTITIES | Rypergeometric series

Journal Article

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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

Optik, ISSN 0030-4026, 05/2019, Volume 184, pp. 277 - 286

The work on this paper focuses on the retrieval of highly dispersive optical solitons that maintain non-local nonlinearity. The extended version of Jacobi's...

Non-local nonlinearity | Jacobi's elliptic function | Highly dispersive solitons | 060.5530 | 060.2310 | 060.4510 | 190.4370 | 190.3270 | OPTICS | KERR LAW NONLINEARITY

Non-local nonlinearity | Jacobi's elliptic function | Highly dispersive solitons | 060.5530 | 060.2310 | 060.4510 | 190.4370 | 190.3270 | OPTICS | KERR LAW NONLINEARITY

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