Mathematical and Computer Modelling, ISSN 0895-7177, 2011, Volume 54, Issue 9, pp. 2109 - 2116

In this paper, the exact traveling wave solutions of the Zhiber–Shabat equation and the related equations: Liouville equation, Dodd–Bullough–Mikhailov (DBM)...

Tzitzeica–Dodd–Bullough (TDB) equation | ( [formula omitted])-expansion method | Zhiber–Shabat equation | Dodd–Bullough–Mikhailov (DBM) equation | Traveling wave solutions | Liouville equation | Tzitzeica-Dodd-Bullough (TDB) equation | Dodd-Bullough-Mikhailov (DBM) equation | Zhiber-Shabat equation | (G'G)-expansion method | (G '/G)-expansion method | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | GORDON EQUATION | EXP-FUNCTION METHOD | EXTENDED TANH METHOD | NONLINEAR EVOLUTION-EQUATIONS

Tzitzeica–Dodd–Bullough (TDB) equation | ( [formula omitted])-expansion method | Zhiber–Shabat equation | Dodd–Bullough–Mikhailov (DBM) equation | Traveling wave solutions | Liouville equation | Tzitzeica-Dodd-Bullough (TDB) equation | Dodd-Bullough-Mikhailov (DBM) equation | Zhiber-Shabat equation | (G'G)-expansion method | (G '/G)-expansion method | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | GORDON EQUATION | EXP-FUNCTION METHOD | EXTENDED TANH METHOD | NONLINEAR EVOLUTION-EQUATIONS

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 2008, Volume 13, Issue 3, pp. 584 - 592

The tanh method and the extended tanh method are used for handling the Zhiber–Shabat equation and the related equations: Liouville equation, sinh-Gordon...

Tzitzeica–Dodd–Bullough equation | The tanh method | Zhiber–Shabat equation | Sinh-Gordon equation | Dodd–Bullough–Mikhailov equation | Liouville equation | Dodd-Bullough-Mikhailov equation | Tzitzeica-Dodd-Bullough equation | Zhiber-Shabat equation | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | SINH-GORDON EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | VARIABLE SEPARATED ODE | the tanh method

Tzitzeica–Dodd–Bullough equation | The tanh method | Zhiber–Shabat equation | Sinh-Gordon equation | Dodd–Bullough–Mikhailov equation | Liouville equation | Dodd-Bullough-Mikhailov equation | Tzitzeica-Dodd-Bullough equation | Zhiber-Shabat equation | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | SINH-GORDON EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | VARIABLE SEPARATED ODE | the tanh method

Journal Article

Ain Shams Engineering Journal, ISSN 2090-4479, 12/2013, Volume 4, Issue 4, pp. 903 - 909

The modified simple equation (MSE) method is thriving in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in engineering and...

Tzitzeica–Dodd–Bullough equation | Nonlinear evolution equations | Modified KdV–Zakharov–Kuznetsov equation | Solitary wave solutions | Modified simple equation method | Exact solutions | Tzitzeica-Dodd-Bullough equation | Modified KdV-Zakharov-Kuznetsov equation

Tzitzeica–Dodd–Bullough equation | Nonlinear evolution equations | Modified KdV–Zakharov–Kuznetsov equation | Solitary wave solutions | Modified simple equation method | Exact solutions | Tzitzeica-Dodd-Bullough equation | Modified KdV-Zakharov-Kuznetsov equation

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 05/2018, Volume 15, Issue 5

We apply the Wick rotation to the Monge-Ampere equation of Tzitzeica graphs and we introduce the Wick-Tzitzeica solitons as complex functions solving the new...

Tzitzeica equation | Wick rotation | Wick-Tzitzeica soliton | Monge-Ampère equation | Tzitzeica surface | Monge-Ampere equation | PHYSICS, MATHEMATICAL | SURFACES

Tzitzeica equation | Wick rotation | Wick-Tzitzeica soliton | Monge-Ampère equation | Tzitzeica surface | Monge-Ampere equation | PHYSICS, MATHEMATICAL | SURFACES

Journal Article

Optik, ISSN 0030-4026, 09/2018, Volume 168, pp. 807 - 816

In this paper, new types of Jacobi elliptic function solutions of Dodd–Bullough–Mikhailov(DBM) and Tzitzeica–Dodd–Bullough(TDB) equations have been obtained...

Tzitzeica–Dodd–Bullough equation | Jacobi elliptic function solutions | Painlevé transformation | Periodic function solutions | Dodd–Bullough–Mikhailov equation | Extended auxiliary equation method | Travelling wave | New exact solutions | Soliton-like solutions | Tzitzeica-Dodd-Bullough equation | ELLIPTIC FUNCTION EXPANSION | Painleve transformation | Dodd-Bullough-Mikhailov equation | SCHRODINGER-TYPE EQUATIONS | EVOLUTION-EQUATIONS | NONLINEAR DIFFERENTIAL-EQUATIONS | (G'/G)-EXPANSION METHOD | OPTICS | TANH-FUNCTION METHOD

Tzitzeica–Dodd–Bullough equation | Jacobi elliptic function solutions | Painlevé transformation | Periodic function solutions | Dodd–Bullough–Mikhailov equation | Extended auxiliary equation method | Travelling wave | New exact solutions | Soliton-like solutions | Tzitzeica-Dodd-Bullough equation | ELLIPTIC FUNCTION EXPANSION | Painleve transformation | Dodd-Bullough-Mikhailov equation | SCHRODINGER-TYPE EQUATIONS | EVOLUTION-EQUATIONS | NONLINEAR DIFFERENTIAL-EQUATIONS | (G'/G)-EXPANSION METHOD | OPTICS | TANH-FUNCTION METHOD

Journal Article

Journal of Modern Optics, ISSN 0950-0340, 09/2017, Volume 64, Issue 16, pp. 1688 - 1692

The properties of Tzitzéica equations in non-linear optics have been the subject of many recent studies. In this article, a new and effective modification of...

Dodd-Bullough-Mikhailov equation | Tzitzéica equation | new exact traveling wave solutions | Tzitzéica-Dodd-Bullough equation | modified Kudryashov method | Tzitzéica–Dodd–Bullough equation | Dodd–Bullough–Mikhailov equation | Tzitzeica equation | ORDER | Tzitzeica-Dodd-Bullough equation | SOLITONS | GENERALIZED FISHER EQUATION | OPTICS | FRACTIONAL DIFFERENTIAL-EQUATIONS | Nonlinear equations | Linear evolution equations | Nonlinear evolution equations | Optics | Evolution | Nonlinear programming | Nonlinear optics

Dodd-Bullough-Mikhailov equation | Tzitzéica equation | new exact traveling wave solutions | Tzitzéica-Dodd-Bullough equation | modified Kudryashov method | Tzitzéica–Dodd–Bullough equation | Dodd–Bullough–Mikhailov equation | Tzitzeica equation | ORDER | Tzitzeica-Dodd-Bullough equation | SOLITONS | GENERALIZED FISHER EQUATION | OPTICS | FRACTIONAL DIFFERENTIAL-EQUATIONS | Nonlinear equations | Linear evolution equations | Nonlinear evolution equations | Optics | Evolution | Nonlinear programming | Nonlinear optics

Journal Article

Mathematical and Computer Modelling, ISSN 0895-7177, 2010, Volume 52, Issue 9, pp. 1834 - 1845

In this work, the ( G ′ G ) -expansion method is applied for constructing more general exact solutions of the three nonlinear evolution equations with physical...

Hyperbolic function solutions | Tzitzéica equation | Tzitzéica–Dodd–Bullough (TDB) equation | [formula omitted]-expansion method | Dodd–Bullough–Mikhailov (DBM) equation | Trigonometric function solutions | Tzitzéica-Dodd-Bullough (TDB) equation | (G'/G)-expansion method | Dodd-Bullough-Mikhailov (DBM) equation | TRANSFORMATION | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | PERTURBATION METHOD | (G '/G)-expansion method | Tzitzeica equation | (G'/G)-EXPANSION METHOD | TRAVELING-WAVE SOLUTIONS | SOLITON-SOLUTIONS | EXP-FUNCTION METHOD | Tzitzeica-Dodd-Bullough (TDB) equation | Employee motivation | Analysis | Methods

Hyperbolic function solutions | Tzitzéica equation | Tzitzéica–Dodd–Bullough (TDB) equation | [formula omitted]-expansion method | Dodd–Bullough–Mikhailov (DBM) equation | Trigonometric function solutions | Tzitzéica-Dodd-Bullough (TDB) equation | (G'/G)-expansion method | Dodd-Bullough-Mikhailov (DBM) equation | TRANSFORMATION | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | PERTURBATION METHOD | (G '/G)-expansion method | Tzitzeica equation | (G'/G)-EXPANSION METHOD | TRAVELING-WAVE SOLUTIONS | SOLITON-SOLUTIONS | EXP-FUNCTION METHOD | Tzitzeica-Dodd-Bullough (TDB) equation | Employee motivation | Analysis | Methods

Journal Article

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 11/2017, Volume 149, pp. 439 - 446

In this paper, using the Painleve property, the traveling wave transformation, and the sine-Gordon expansion method (SGEM), the Tzitzéica type evolution...

Sine-Gordon expansion method | Tzitzéica type equations | Nonlinear optics | Traveling wave solutions | Tzitzeica type equations | (G'/G)-EXPANSION METHOD | ZHIBER-SHABAT EQUATION | EVOLUTION-EQUATIONS | OPTICS | SOLITON

Sine-Gordon expansion method | Tzitzéica type equations | Nonlinear optics | Traveling wave solutions | Tzitzeica type equations | (G'/G)-EXPANSION METHOD | ZHIBER-SHABAT EQUATION | EVOLUTION-EQUATIONS | OPTICS | SOLITON

Journal Article

9.
Full Text
New optical solitons of Tzitzeíca type evolution equations using extended trial approach

Optical and Quantum Electronics, ISSN 0306-8919, 3/2018, Volume 50, Issue 3, pp. 1 - 13

The properties of Tzitzeíca equations in nonlinear optics have been the discussion of many recent studies. In this article, a new and productive implementation...

Extended trial equation method | Tzitzeíca equation | Dodd–Bullough–Mikhailov equation | Optical solitons | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Computer Communication Networks | Physics | Electrical Engineering | Tzitzeíca–Dodd–Bullough equation | Tzitzeica-Dodd-Bullough equation | TRAVELING-WAVE SOLUTIONS | NONLINEAR EQUATIONS | Tzitzei caequation | Dodd-Bullough-Mikhailov equation | OPTICS | ENGINEERING, ELECTRICAL & ELECTRONIC | Management science

Extended trial equation method | Tzitzeíca equation | Dodd–Bullough–Mikhailov equation | Optical solitons | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Computer Communication Networks | Physics | Electrical Engineering | Tzitzeíca–Dodd–Bullough equation | Tzitzeica-Dodd-Bullough equation | TRAVELING-WAVE SOLUTIONS | NONLINEAR EQUATIONS | Tzitzei caequation | Dodd-Bullough-Mikhailov equation | OPTICS | ENGINEERING, ELECTRICAL & ELECTRONIC | Management science

Journal Article

Optical and Quantum Electronics, ISSN 0306-8919, 08/2017, Volume 49, Issue 8

The paper deals with the Tzitzeica type nonlinear evolution equations arising in nonlinear optics and their new exact solutions. First, through the use of the...

Modified version of improved tan (Φ(ξ) / 2) -expansion method | Painlevé transformation | New exact solutions | Lie symmetry method | Tzitzéica type nonlinear evolution equations | Tzitzeica type nonlinear evolution equations | QUANTUM SCIENCE & TECHNOLOGY | Painleve transformation | BISWAS-MILOVIC EQUATION | SCHRODINGERS EQUATION | DARK | DE-VRIES EQUATION | EVOLUTION-EQUATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | TRAVELING-WAVE SOLUTIONS | SOLITON-SOLUTIONS | LIE SYMMETRY ANALYSIS | EXP-FUNCTION METHOD | Modified version of improved tan(Phi(xi)/2)-expansion method | OPTICS | POWER-LAW NONLINEARITY

Modified version of improved tan (Φ(ξ) / 2) -expansion method | Painlevé transformation | New exact solutions | Lie symmetry method | Tzitzéica type nonlinear evolution equations | Tzitzeica type nonlinear evolution equations | QUANTUM SCIENCE & TECHNOLOGY | Painleve transformation | BISWAS-MILOVIC EQUATION | SCHRODINGERS EQUATION | DARK | DE-VRIES EQUATION | EVOLUTION-EQUATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | TRAVELING-WAVE SOLUTIONS | SOLITON-SOLUTIONS | LIE SYMMETRY ANALYSIS | EXP-FUNCTION METHOD | Modified version of improved tan(Phi(xi)/2)-expansion method | OPTICS | POWER-LAW NONLINEARITY

Journal Article

Zeitschrift für Naturforschung A, ISSN 0932-0784, 10/2018, Volume 73, Issue 10, pp. 883 - 892

We use a simple method that leads to the integrals involved in obtaining the travelling-wave solutions of wave equations with one and two exponential...

Tzitzéica | Weierstrass Function | 02.30.Ik | sine-Gordon | Dodd-Bullough | Liouville Equation | sinh-Gordon | 02.30.Hq | 04.20.Jb | Dodd-Bullough-Mikhailov | TRANSFORMATION | Tzitzeica | PHYSICS, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | DIFFERENTIAL-EQUATIONS | EVOLUTION | MODELS

Tzitzéica | Weierstrass Function | 02.30.Ik | sine-Gordon | Dodd-Bullough | Liouville Equation | sinh-Gordon | 02.30.Hq | 04.20.Jb | Dodd-Bullough-Mikhailov | TRANSFORMATION | Tzitzeica | PHYSICS, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | DIFFERENTIAL-EQUATIONS | EVOLUTION | MODELS

Journal Article

Optical and Quantum Electronics, ISSN 0306-8919, 1/2018, Volume 50, Issue 1, pp. 1 - 12

In this article, two newly developed methods, namely the exp$$(-~\Phi (\xi ))$$ (-Φ(ξ)) method and the modified Kudryashov method are used to extract the exact...

Exp $$(-~\Phi (\xi ))$$ ( - Φ ( ξ ) ) method | Optics, Lasers, Photonics, Optical Devices | Exact solutions | Nonlinear Phi-4 equation | Characterization and Evaluation of Materials | Conformable time-fractional derivative | Modified Kudryashov method | Computer Communication Networks | Physics | Electrical Engineering | Exp(-Φ(ξ)) method | QUANTUM SCIENCE & TECHNOLOGY | TZITZEICA TYPE EQUATIONS | EXP-FUNCTION | DIFFERENTIAL-EQUATIONS | Exp(-phi(xi)) method | EVOLUTION-EQUATIONS | MODEL | ENGINEERING, ELECTRICAL & ELECTRONIC | TRAVELING-WAVE SOLUTIONS | CAHN-ALLEN | OPTICS

Exp $$(-~\Phi (\xi ))$$ ( - Φ ( ξ ) ) method | Optics, Lasers, Photonics, Optical Devices | Exact solutions | Nonlinear Phi-4 equation | Characterization and Evaluation of Materials | Conformable time-fractional derivative | Modified Kudryashov method | Computer Communication Networks | Physics | Electrical Engineering | Exp(-Φ(ξ)) method | QUANTUM SCIENCE & TECHNOLOGY | TZITZEICA TYPE EQUATIONS | EXP-FUNCTION | DIFFERENTIAL-EQUATIONS | Exp(-phi(xi)) method | EVOLUTION-EQUATIONS | MODEL | ENGINEERING, ELECTRICAL & ELECTRONIC | TRAVELING-WAVE SOLUTIONS | CAHN-ALLEN | OPTICS

Journal Article

Optik, ISSN 0030-4026, 02/2018, Volume 154, pp. 393 - 397

In this paper, we consider the Tzitzéica type equations and establish the travelling wave transformation which turns the nonlinear evolution equations into the...

Tzitzéica type equations | Travelling wave transformation | Exponential rational function method | Exact solutions | Tzitzeica type equations | TRAVELING-WAVE SOLUTIONS | SOLITONS | DIFFERENTIAL-EQUATIONS | OPTICS

Tzitzéica type equations | Travelling wave transformation | Exponential rational function method | Exact solutions | Tzitzeica type equations | TRAVELING-WAVE SOLUTIONS | SOLITONS | DIFFERENTIAL-EQUATIONS | OPTICS

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 02/2014, Volume 34, Issue 2, pp. 557 - 566

We use a novel transformation of the reduced Ostrovsky equation to the integrable Tzitzeica equation and prove global existence of small-norm solutions in...

Conserved quantities | Global existence | Tzitzéica equation | Reduced Ostrovsky equation | Wave breaking | MATHEMATICS | Tzitzeica equation | MATHEMATICS, APPLIED | global existence | CAUCHY-PROBLEM | SHORT-PULSE | WELL-POSEDNESS | conserved quantities | SCATTERING | wave breaking | BACKLUND TRANSFORMATION

Conserved quantities | Global existence | Tzitzéica equation | Reduced Ostrovsky equation | Wave breaking | MATHEMATICS | Tzitzeica equation | MATHEMATICS, APPLIED | global existence | CAUCHY-PROBLEM | SHORT-PULSE | WELL-POSEDNESS | conserved quantities | SCATTERING | wave breaking | BACKLUND TRANSFORMATION

Journal Article

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 11/2017, Volume 148, pp. 85 - 89

The Tzitzéica type equations arising in nonlinear optics, including the Tzitzéica, Dodd–Bullough–Mikhailov, and Tzitzéica–Dodd–Bullough equations are solved...

Novel exponential rational function method | Tzitzéica type equations | New exact solutions | Nonlinear optics | Tzitzeica type equations | SOLITON-SOLUTIONS | PERIODIC-WAVE | OPTICS | NONLINEAR SCHRODINGER-EQUATION | OPTICAL SOLITONS

Novel exponential rational function method | Tzitzéica type equations | New exact solutions | Nonlinear optics | Tzitzeica type equations | SOLITON-SOLUTIONS | PERIODIC-WAVE | OPTICS | NONLINEAR SCHRODINGER-EQUATION | OPTICAL SOLITONS

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 2015, Volume 2015, Issue 8, pp. 2141 - 2167

Based on solutions of the stationary zero-curvature equation associated with a 3 x 3 matrix spectral problem, we introduce a trigonal curve related to the...

MATHEMATICS | PERIODIC-SOLUTIONS | DARBOUX TRANSFORMATION | SYMMETRIES | SOLITONS | TRIGONAL CURVES | BOUSSINESQ | DECOMPOSITION | ABELIAN FUNCTIONS | TZITZEICA | Functions (mathematics) | Asymptotic properties | Mathematical analysis | Differentials | Meromorphic functions | Spectra | Representations

MATHEMATICS | PERIODIC-SOLUTIONS | DARBOUX TRANSFORMATION | SYMMETRIES | SOLITONS | TRIGONAL CURVES | BOUSSINESQ | DECOMPOSITION | ABELIAN FUNCTIONS | TZITZEICA | Functions (mathematics) | Asymptotic properties | Mathematical analysis | Differentials | Meromorphic functions | Spectra | Representations

Journal Article

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 08/2017, Volume 142, pp. 394 - 400

In this study, exact solutions of the nonlinear partial differential equations have been examined. The Tzitzeica-Dodd-Bullough, the nonlinear telegraph and the...

Tzitzeica-Dodd-Bullough equation | Nonlinear telegraph equation | The trial equation method | Generalized Benjamin-Bona-Mahony equation | SOLITON-SOLUTIONS | OPTICS | Fluid dynamics | Differential equations

Tzitzeica-Dodd-Bullough equation | Nonlinear telegraph equation | The trial equation method | Generalized Benjamin-Bona-Mahony equation | SOLITON-SOLUTIONS | OPTICS | Fluid dynamics | Differential equations

Journal Article

Balkan Journal of Geometry and its Applications, ISSN 1224-2780, 2014, Volume 19, Issue 2, pp. 11 - 22

We discuss the Tzitzeica equation and the spectral properties associated with its Lax operator L. We prove that the continuous spectrum of L is rotated with...

Tzitzeica equation | Riemann-Hilbert problem | Resolvent of lax operator | MATHEMATICS | INVERSE SCATTERING | resolvent of Lax operator | Differential equations, Partial | Transformations (Mathematics) | Analysis

Tzitzeica equation | Riemann-Hilbert problem | Resolvent of lax operator | MATHEMATICS | INVERSE SCATTERING | resolvent of Lax operator | Differential equations, Partial | Transformations (Mathematics) | Analysis

Journal Article

Journal of Geometry and Symmetry in Physics, ISSN 1312-5192, 2015, Volume 37, pp. 1 - 24

J. Geom. Symm. Phys. {\bf 37}, 1--24 (2015) We analyze several types of soliton solutions to a family of Tzitzeica equations. To this end we use two methods...

Hirota method | Zakharov-Shabat dressing method | Tzitzeica equations | singular soliton solutions | Physics - Exactly Solvable and Integrable Systems

Hirota method | Zakharov-Shabat dressing method | Tzitzeica equations | singular soliton solutions | Physics - Exactly Solvable and Integrable Systems

Journal Article

应用数学学报：英文版, ISSN 0168-9673, 2016, Volume 32, Issue 2, pp. 461 - 468

In this work, it is aimed to find one- and two-soliton solutions to nonlinear Tzitzeica-Dodd-Bullough （TDB） equation. Since the double exp-function method has...

74J35 | double exp-function method | Tzitzeica-Dodd-Bullough equation | 33F10 | solitary waves | one-soliton | Theoretical, Mathematical and Computational Physics | two-soliton | Mathematics | Applications of Mathematics | Math Applications in Computer Science | 35Q51

74J35 | double exp-function method | Tzitzeica-Dodd-Bullough equation | 33F10 | solitary waves | one-soliton | Theoretical, Mathematical and Computational Physics | two-soliton | Mathematics | Applications of Mathematics | Math Applications in Computer Science | 35Q51

Journal Article

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