Physics Letters A, ISSN 0375-9601, 2009, Volume 373, Issue 21, pp. 1844 - 1846

In this work, four ( 2 + 1 ) -dimensional nonlinear evolution equations, generated by the Jaulent–Miodek hierarchy, are investigated. The necessary condition...

Multiple kink solutions | Multiple singular kink solutions | Nonlinear [formula omitted]-dimensional equation | Hirota bilinear method | Nonlinear (2 + 1)-dimensional equation | HIROTA 3-SOLITON CONDITION | PHYSICS, MULTIDISCIPLINARY | BURGERS EQUATIONS | FRONT SOLUTIONS | SEARCH | Nonlinear (2+1)-dimensional equation | SHALLOW-WATER WAVES | EVOLUTION-EQUATIONS | TANH-COTH METHOD | KP EQUATION | BILINEAR EQUATIONS | N-SOLITON SOLUTION

Multiple kink solutions | Multiple singular kink solutions | Nonlinear [formula omitted]-dimensional equation | Hirota bilinear method | Nonlinear (2 + 1)-dimensional equation | HIROTA 3-SOLITON CONDITION | PHYSICS, MULTIDISCIPLINARY | BURGERS EQUATIONS | FRONT SOLUTIONS | SEARCH | Nonlinear (2+1)-dimensional equation | SHALLOW-WATER WAVES | EVOLUTION-EQUATIONS | TANH-COTH METHOD | KP EQUATION | BILINEAR EQUATIONS | N-SOLITON SOLUTION

Journal Article

Physics Letters A, ISSN 0375-9601, 2008, Volume 373, Issue 1, pp. 83 - 88

Utilizing the Hirota bilinear method, an N-soliton solution for a ( 2 + 1 ) -dimensional nonlinear evolution equation is obtained. Further, generalized double...

[formula omitted]-dimensional nonlinear evolution equation | Double Wronskian determinant | Rational solution | N-soliton solution | (2 + 1)-dimensional nonlinear evolution equation | TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | QUASI-PERIODIC SOLUTIONS | DECOMPOSITION | (2+1)-dimensional nonlinear evolution equation

[formula omitted]-dimensional nonlinear evolution equation | Double Wronskian determinant | Rational solution | N-soliton solution | (2 + 1)-dimensional nonlinear evolution equation | TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | QUASI-PERIODIC SOLUTIONS | DECOMPOSITION | (2+1)-dimensional nonlinear evolution equation

Journal Article

3.
Full Text
A two-mode coupled Korteweg–de Vries: multiple-soliton solutions and other exact solutions

Nonlinear Dynamics, ISSN 0924-090X, 10/2017, Volume 90, Issue 1, pp. 371 - 377

In this paper, we introduce the new nonlinear two-mode coupled Korteweg–de Vries. We find the necessary conditions of dispersion parameter and the nonlinearity...

Engineering | Vibration, Dynamical Systems, Control | Simplified Hirota method | N -soliton solutions | Classical Mechanics | Automotive Engineering | Two-mode coupled Korteweg–de Vries | Mechanical Engineering | N-soliton solutions | Two-mode coupled Korteweg-de Vries | BOUSSINESQ EQUATION | MECHANICS | BURGERS-TYPE | KDV EQUATION | WAVE SOLUTIONS | COLLISIONS | ENGINEERING, MECHANICAL | Parameters | Mathematical analysis | Exact solutions | Coupled modes | Nonlinearity | Trigonometric functions | Solitary waves

Engineering | Vibration, Dynamical Systems, Control | Simplified Hirota method | N -soliton solutions | Classical Mechanics | Automotive Engineering | Two-mode coupled Korteweg–de Vries | Mechanical Engineering | N-soliton solutions | Two-mode coupled Korteweg-de Vries | BOUSSINESQ EQUATION | MECHANICS | BURGERS-TYPE | KDV EQUATION | WAVE SOLUTIONS | COLLISIONS | ENGINEERING, MECHANICAL | Parameters | Mathematical analysis | Exact solutions | Coupled modes | Nonlinearity | Trigonometric functions | Solitary waves

Journal Article

International Journal of Modern Physics B, ISSN 0217-9792, 10/2019, Volume 33, Issue 27, p. 1950319

Based on the Hirota bilinear form, lump-type solutions, interaction solutions and periodic wave solutions of a (3 + 1)-dimensional Korteweg–de Vries (KdV)...

periodic wave solutions | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | (3+1)-Dimensional KdV equation | lump-type solutions | Hirota bilinear form | interaction solutions | PHYSICS, MATHEMATICAL | N-SOLITON SOLUTIONS

periodic wave solutions | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | (3+1)-Dimensional KdV equation | lump-type solutions | Hirota bilinear form | interaction solutions | PHYSICS, MATHEMATICAL | N-SOLITON SOLUTIONS

Journal Article

ADVANCES IN DIFFERENCE EQUATIONS, ISSN 1687-1847, 08/2019, Volume 2019, Issue 1, pp. 1 - 11

In this work, the (2 + 1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation is investigated. Hirota's bilinear method is used to determine the...

Interaction solution | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRABILITY | NNV equation | Hirota bilinear method | N-soliton solution | TRANSFORM | HIERARCHY | Solitary waves | Wave propagation

Interaction solution | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRABILITY | NNV equation | Hirota bilinear method | N-soliton solution | TRANSFORM | HIERARCHY | Solitary waves | Wave propagation

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 217, Issue 21, pp. 8722 - 8730

A set of sufficient conditions consisting of systems of linear partial differential equations is obtained which guarantees that the Wronskian determinant...

Negatons | Positons | (3 + 1)-dimensional Jimbo–Miwa equation | Rational solutions | Wronskian form | (3 + 1)-dimensional Jimbo-Miwa equation | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | (3+1)-dimensional Jimbo-Miwa equation | N-SOLITON SOLUTION | Determinants | Mathematical models | Partial differential equations | Computation | Mathematical analysis | Solitons

Negatons | Positons | (3 + 1)-dimensional Jimbo–Miwa equation | Rational solutions | Wronskian form | (3 + 1)-dimensional Jimbo-Miwa equation | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | (3+1)-dimensional Jimbo-Miwa equation | N-SOLITON SOLUTION | Determinants | Mathematical models | Partial differential equations | Computation | Mathematical analysis | Solitons

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 10/2018, Volume 132, pp. 45 - 54

A 3 × 3 matrix spectral problem is introduced and its associated AKNS integrable hierarchy with four components is generated. From this spectral problem, a...

[formula omitted]-soliton solution | Riemann–Hilbert problem | Integrable hierarchy | N-soliton solution | MATHEMATICS | Riemann-Hilbert problem | INTEGRABLE SYSTEMS | EQUATIONS | HAMILTONIAN STRUCTURES | SEMIDIRECT SUMS | PHYSICS, MATHEMATICAL | HIERARCHY

[formula omitted]-soliton solution | Riemann–Hilbert problem | Integrable hierarchy | N-soliton solution | MATHEMATICS | Riemann-Hilbert problem | INTEGRABLE SYSTEMS | EQUATIONS | HAMILTONIAN STRUCTURES | SEMIDIRECT SUMS | PHYSICS, MATHEMATICAL | HIERARCHY

Journal Article

8.
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Riemann–Hilbert approach and N-soliton solutions for a generalized Sasa–Satsuma equation

Wave Motion, ISSN 0165-2125, 01/2016, Volume 60, pp. 62 - 72

A generalized Sasa–Satsuma equation on the line is studied via the Riemann–Hilbert approach. Firstly we derive a Lax pair associated with a 3×3 matrix spectral...

Riemann–Hilbert approach | Generalized Sasa–Satsuma equation | [formula omitted]-soliton solutions | N-soliton solutions | Generalized Sasa-Satsuma equation | Riemann-Hilbert approach | ACOUSTICS | MECHANICS | PHYSICS, MULTIDISCIPLINARY

Riemann–Hilbert approach | Generalized Sasa–Satsuma equation | [formula omitted]-soliton solutions | N-soliton solutions | Generalized Sasa-Satsuma equation | Riemann-Hilbert approach | ACOUSTICS | MECHANICS | PHYSICS, MULTIDISCIPLINARY

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 12/2016, Volume 72, Issue 11, pp. 2685 - 2693

This paper deals with a (2+1)-dimensional nonlinear evolution equation (NLEE) generated by the Jaulent–Miodek hierarchy for nonlinear water waves via the...

Hirota’s bilinear method | Nonlinear evolution equation | Nonlinear water waves | Rational solutions | Jaulent–Miodek hierarchy | Pfaffian | Hirota's bilinear method | MATHEMATICS, APPLIED | SCHRODINGER-EQUATION | BILINEAR BACKLUND-TRANSFORMATIONS | COLLISIONS | ROGUE WAVES | Jaulent-Miodek hierarchy | EVOLUTION EQUATION | DYNAMICS | N-SOLITON SOLUTION | Water waves | Models | Fluid dynamics | Hierarchies | Simplification | Computer simulation | Mathematical analysis | Nonlinear evolution equations | Nonlinearity | Mathematical models

Hirota’s bilinear method | Nonlinear evolution equation | Nonlinear water waves | Rational solutions | Jaulent–Miodek hierarchy | Pfaffian | Hirota's bilinear method | MATHEMATICS, APPLIED | SCHRODINGER-EQUATION | BILINEAR BACKLUND-TRANSFORMATIONS | COLLISIONS | ROGUE WAVES | Jaulent-Miodek hierarchy | EVOLUTION EQUATION | DYNAMICS | N-SOLITON SOLUTION | Water waves | Models | Fluid dynamics | Hierarchies | Simplification | Computer simulation | Mathematical analysis | Nonlinear evolution equations | Nonlinearity | Mathematical models

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 4/2019, Volume 96, Issue 1, pp. 789 - 800

In this paper, a new coupled Gerdjikov–Ivanov derivative nonlinear Schrödinger equation is proposed and its integrability aspects are studied by utilizing the...

Engineering | Vibration, Dynamical Systems, Control | Soliton dynamics | Integrability aspects | Spectral structure | Classical Mechanics | Automotive Engineering | Coupled Gerdjikov–Ivanov equation | Mechanical Engineering | Inverse scattering transform | MECHANICS | FORM | BOUSSINESQ | SYSTEMS | Coupled Gerdjikov-Ivanov equation | N-SOLITON SOLUTIONS | ENGINEERING, MECHANICAL | HIERARCHY

Engineering | Vibration, Dynamical Systems, Control | Soliton dynamics | Integrability aspects | Spectral structure | Classical Mechanics | Automotive Engineering | Coupled Gerdjikov–Ivanov equation | Mechanical Engineering | Inverse scattering transform | MECHANICS | FORM | BOUSSINESQ | SYSTEMS | Coupled Gerdjikov-Ivanov equation | N-SOLITON SOLUTIONS | ENGINEERING, MECHANICAL | HIERARCHY

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 02/2019, Volume 77, Issue 4, pp. 947 - 966

In this paper, the N-soliton solution is constructed for the (2+1)-dimensional generalized Hirota–Satsuma–Ito equation, from which some localized waves such as...

Generalized Hirota–Satsuma–Ito equation | [formula omitted]-soliton solution | Lump soliton | Periodic soliton | N-soliton solution | RATIONAL SOLUTIONS | MATHEMATICS, APPLIED | DARBOUX TRANSFORMATION | BOUSSINESQ EQUATION | ORDER ROGUE WAVE | LUMP-KINK SOLUTIONS | RESONANCE STRIPE SOLITONS | BACKLUND TRANSFORMATION | Generalized Hirota-Satsuma-Ito equation | RESIDUAL SYMMETRIES | (3+1)-DIMENSIONAL JIMBO-MIWA | VARIABLE SEPARATION SOLUTIONS | Nonlinear equations | Wave interaction | Interaction parameters | Mathematical analysis | Solitary waves | Wave equations

Generalized Hirota–Satsuma–Ito equation | [formula omitted]-soliton solution | Lump soliton | Periodic soliton | N-soliton solution | RATIONAL SOLUTIONS | MATHEMATICS, APPLIED | DARBOUX TRANSFORMATION | BOUSSINESQ EQUATION | ORDER ROGUE WAVE | LUMP-KINK SOLUTIONS | RESONANCE STRIPE SOLITONS | BACKLUND TRANSFORMATION | Generalized Hirota-Satsuma-Ito equation | RESIDUAL SYMMETRIES | (3+1)-DIMENSIONAL JIMBO-MIWA | VARIABLE SEPARATION SOLUTIONS | Nonlinear equations | Wave interaction | Interaction parameters | Mathematical analysis | Solitary waves | Wave equations

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 08/2014, Volume 26, Issue 7, p. 1430006

This is a continuation of [Notes on solutions in Wronskian form to soliton equations: Korteweg–de Vries-type, arXiv:nlin.SI/0603008]. In the present paper, we...

breathers | dynamics | Wronskian | The modified Korteweg-de Vries equation | rational solutions | FORM | PHYSICS, MATHEMATICAL | DEVRIES | WAVES | MODELS | MULTIPLE COLLISIONS | ION-ACOUSTIC SOLITON | N-SOLITON SOLUTIONS | PROPAGATION

breathers | dynamics | Wronskian | The modified Korteweg-de Vries equation | rational solutions | FORM | PHYSICS, MATHEMATICAL | DEVRIES | WAVES | MODELS | MULTIPLE COLLISIONS | ION-ACOUSTIC SOLITON | N-SOLITON SOLUTIONS | PROPAGATION

Journal Article

PHYSICA SCRIPTA, ISSN 0031-8949, 09/2019, Volume 94, Issue 9, p. 95203

This paper studies the N-soliton solutions of the generalized nonlinear Schrodinger equation. Firstly, the spectral analysis of a Lax pair is carried out....

DARBOUX TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | Riemann-Hilbert approach | the generalized nonlinear Schrodinger equation N-soliton solutions

DARBOUX TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | Riemann-Hilbert approach | the generalized nonlinear Schrodinger equation N-soliton solutions

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 1/2012, Volume 67, Issue 2, pp. 1023 - 1030

Under investigation in this paper is a generalized variable-coefficient forced Korteweg–de Vries equation, which can describe the shallow-water waves, internal...

Engineering | Vibration, Dynamical Systems, Control | Lax pair | Hirota bilinear method | Mechanics | Automotive Engineering | Variable-coefficient forced Korteweg–de Vries equation in fluids | Mechanical Engineering | Soliton solutions in the Wronskian form | Symbolic computation | Variable-coefficient forced Korteweg-de Vries equation in fluids | TODA LATTICE EQUATION | BOUSSINESQ EQUATION | DEVRIES EQUATION | FORM | ION-ACOUSTIC-WAVES | NEBULONS | MODEL | ENGINEERING, MECHANICAL | BACKLUND TRANSFORMATION | MECHANICS | N-SOLITON SOLUTION | Fluid dynamics | Aeronautics | Water waves | Coefficients | Solitary waves | Gravitational waves | Gravity waves | Fluids | Computational fluid dynamics | Mathematical analysis | Solitons | Fluid flow | Mathematical models | Transformations

Engineering | Vibration, Dynamical Systems, Control | Lax pair | Hirota bilinear method | Mechanics | Automotive Engineering | Variable-coefficient forced Korteweg–de Vries equation in fluids | Mechanical Engineering | Soliton solutions in the Wronskian form | Symbolic computation | Variable-coefficient forced Korteweg-de Vries equation in fluids | TODA LATTICE EQUATION | BOUSSINESQ EQUATION | DEVRIES EQUATION | FORM | ION-ACOUSTIC-WAVES | NEBULONS | MODEL | ENGINEERING, MECHANICAL | BACKLUND TRANSFORMATION | MECHANICS | N-SOLITON SOLUTION | Fluid dynamics | Aeronautics | Water waves | Coefficients | Solitary waves | Gravitational waves | Gravity waves | Fluids | Computational fluid dynamics | Mathematical analysis | Solitons | Fluid flow | Mathematical models | Transformations

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 09/2016, Volume 59, pp. 115 - 121

In this paper, by employing the Hirota’s bilinear method, we construct the N-soliton solution for an integrable nonlocal discrete focusing nonlinear...

Hirota’s bilinear method | Discrete nonlocal Schrödinger equation | [formula omitted]-soliton solution | Hirota's bilinear method | N-soliton solution

Hirota’s bilinear method | Discrete nonlocal Schrödinger equation | [formula omitted]-soliton solution | Hirota's bilinear method | N-soliton solution

Journal Article

Modern Physics Letters B, ISSN 0217-9849, 01/2019, Volume 33, Issue 2, p. 1950002

In this paper, we construct the Riemann-Hilbert problem to the Lax pair of Chen-Lee- Liu (CLL) equation. As far as we know, many researchers have studied...

Chen-Lee-Liu equation | N-soliton | Riemann-Hilbert approach | PHYSICS, CONDENSED MATTER | INTEGRABILITY | PHYSICS, APPLIED | SYSTEMS | PHYSICS, MATHEMATICAL

Chen-Lee-Liu equation | N-soliton | Riemann-Hilbert approach | PHYSICS, CONDENSED MATTER | INTEGRABILITY | PHYSICS, APPLIED | SYSTEMS | PHYSICS, MATHEMATICAL

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2012, Volume 219, Issue 5, pp. 2601 - 2610

More general Wronskian conditions are constructed for the (3+1)-dimensional Jimbo–Miwa equation. As a result, the generalized Wronskian solutions including...

(3 + 1)-Dimensional Jimbo–Miwa equation | Generalized Wronskian solutions | Wronskian technique | Hirota bilinear form | (3 + 1)-Dimensional Jimbo-Miwa equation | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | FORM | (3+1)-Dimensional Jimbo-Miwa equation | N-SOLITON SOLUTION | COMPLEXITON SOLUTIONS

(3 + 1)-Dimensional Jimbo–Miwa equation | Generalized Wronskian solutions | Wronskian technique | Hirota bilinear form | (3 + 1)-Dimensional Jimbo-Miwa equation | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | FORM | (3+1)-Dimensional Jimbo-Miwa equation | N-SOLITON SOLUTION | COMPLEXITON SOLUTIONS

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 7/2014, Volume 77, Issue 1, pp. 135 - 143

With symbolic computation, this paper investigates some integrable properties of a two-dimensional generalization of the Korteweg-de Vries equation, i.e., the...

Engineering | Vibration, Dynamical Systems, Control | Bell-polynomial manipulation | Bilinear Bäcklund transformation | Wronskian solution | Mechanics | Automotive Engineering | Mechanical Engineering | Symbolic computation | Bogoyavlensky–Konoplechenko model | N$$ N -soliton solution | N N -soliton solution | Bogoyavlensky-Konoplechenko model | BOUSSINESQ EQUATION | EXPLICIT SOLUTIONS | QUASI-PERIODIC SOLUTIONS | N-soliton solution | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, MECHANICAL | BACKLUND TRANSFORMATION | MULTISOLITON SOLUTIONS | MECHANICS | SOLITON-SOLUTIONS | PETVIASHVILI EQUATIONS | Bilinear Backlund transformation | WAVE-EQUATION | Wave propagation | Resveratrol | Traffic regulations | Polynomials | Riemann waves | Computation | Solitary waves | Mathematical analysis | Mathematical models | Transformations | Representations

Engineering | Vibration, Dynamical Systems, Control | Bell-polynomial manipulation | Bilinear Bäcklund transformation | Wronskian solution | Mechanics | Automotive Engineering | Mechanical Engineering | Symbolic computation | Bogoyavlensky–Konoplechenko model | N$$ N -soliton solution | N N -soliton solution | Bogoyavlensky-Konoplechenko model | BOUSSINESQ EQUATION | EXPLICIT SOLUTIONS | QUASI-PERIODIC SOLUTIONS | N-soliton solution | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, MECHANICAL | BACKLUND TRANSFORMATION | MULTISOLITON SOLUTIONS | MECHANICS | SOLITON-SOLUTIONS | PETVIASHVILI EQUATIONS | Bilinear Backlund transformation | WAVE-EQUATION | Wave propagation | Resveratrol | Traffic regulations | Polynomials | Riemann waves | Computation | Solitary waves | Mathematical analysis | Mathematical models | Transformations | Representations

Journal Article

Zeitschrift für Naturforschung A, ISSN 0932-0784, 01/2019, Volume 74, Issue 2, pp. 139 - 145

Under investigation in this article is the integrable spin-1 Gross–Pitaevskii (SGP) equations, which can be used to describe light transmission in bimodal...

Riemann–Hilbert Problem (RHP) | Inverse Scattering Transform | 02.30.Ik | Soliton Solution | 05.45.Yv | Integrable Spin-1 Gross–Pitaevskii (SGP) Equations | 02.30.Jr | 04.20.Jb | Integrable Spin-1 Gross-Pitaevskii (SGP) Equations | Riemann-Hilbert Problem (RHP) | PHYSICS, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | NONLINEAR SCHRODINGER-EQUATION | N-SOLITON SOLUTIONS

Riemann–Hilbert Problem (RHP) | Inverse Scattering Transform | 02.30.Ik | Soliton Solution | 05.45.Yv | Integrable Spin-1 Gross–Pitaevskii (SGP) Equations | 02.30.Jr | 04.20.Jb | Integrable Spin-1 Gross-Pitaevskii (SGP) Equations | Riemann-Hilbert Problem (RHP) | PHYSICS, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | NONLINEAR SCHRODINGER-EQUATION | N-SOLITON SOLUTIONS

Journal Article

NONLINEAR DYNAMICS, ISSN 0924-090X, 10/2019, Volume 98, Issue 2, pp. 1275 - 1286

The 2+1-dimensional Sawada-Kotera equation is an important physical model. Here, by taking a long limit and restricting a conjugation condition to the related...

RATIONAL SOLUTIONS | High-order breather solution | M-lump solution | MECHANICS | Sawada-Kotera equation | Hirota bilinear method | Hybrid solution | WAVE SOLUTIONS | N-SOLITON SOLUTIONS | ENGINEERING, MECHANICAL | BACKLUND TRANSFORMATION | Forests and forestry | Numerical analysis

RATIONAL SOLUTIONS | High-order breather solution | M-lump solution | MECHANICS | Sawada-Kotera equation | Hirota bilinear method | Hybrid solution | WAVE SOLUTIONS | N-SOLITON SOLUTIONS | ENGINEERING, MECHANICAL | BACKLUND TRANSFORMATION | Forests and forestry | Numerical analysis

Journal Article

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