Computers and Mathematics with Applications, ISSN 0898-1221, 11/2016, Volume 72, Issue 9, pp. 2486 - 2504

In this paper, a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation is investigated, which can be used to describe weakly dispersive waves...

Riemann theta function | Soliton solution | A [formula omitted]-dimensional generalized B-type Kadomtsev–Petviashvili equation | Periodic solution | Bell polynomials | A (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation | DIMENSIONS | MATHEMATICS, APPLIED | SYMMETRIES | Kadomtsev-Petviashvili equation | NONLINEAR EVOLUTION-EQUATIONS | DARBOUX TRANSFORMATIONS | A (3+1)-dimensional generalized B-type | RATIONAL CHARACTERISTICS | Fluid dynamics | Wave propagation | Amplitudes | Computational fluid dynamics | Asymptotic properties | Mathematical analysis | Mathematical models | Polynomials | Combinatorial analysis

Riemann theta function | Soliton solution | A [formula omitted]-dimensional generalized B-type Kadomtsev–Petviashvili equation | Periodic solution | Bell polynomials | A (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation | DIMENSIONS | MATHEMATICS, APPLIED | SYMMETRIES | Kadomtsev-Petviashvili equation | NONLINEAR EVOLUTION-EQUATIONS | DARBOUX TRANSFORMATIONS | A (3+1)-dimensional generalized B-type | RATIONAL CHARACTERISTICS | Fluid dynamics | Wave propagation | Amplitudes | Computational fluid dynamics | Asymptotic properties | Mathematical analysis | Mathematical models | Polynomials | Combinatorial analysis

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 08/2017, Volume 74, Issue 3, pp. 556 - 563

Under investigation in this work is a generalized (3+1)-dimensional Kadomtsev–Petviashvili (GKP) equation, which can describe many nonlinear phenomena in fluid...

Bell’s polynomials | Rogue waves | Breather waves | Solitary waves | A generalized ([formula omitted])-dimensional Kadomtsev–Petviashvili equation | A generalized (3+1)-dimensional Kadomtsev–Petviashvili equation | Bell's polynomials | MATHEMATICS, APPLIED | FLUID-DYNAMICS | (2+1)-DIMENSIONAL BOUSSINESQ EQUATION | NONLINEAR SCHRODINGER-EQUATION | GEOMETRIC APPROACH | ITO EQUATION | LIE SYMMETRIES | SYSTEMS | A generalized (3+1)-dimensional Kadomtsev-Petviashvili equation | RATIONAL CHARACTERISTICS | Water waves | Fluid dynamics

Bell’s polynomials | Rogue waves | Breather waves | Solitary waves | A generalized ([formula omitted])-dimensional Kadomtsev–Petviashvili equation | A generalized (3+1)-dimensional Kadomtsev–Petviashvili equation | Bell's polynomials | MATHEMATICS, APPLIED | FLUID-DYNAMICS | (2+1)-DIMENSIONAL BOUSSINESQ EQUATION | NONLINEAR SCHRODINGER-EQUATION | GEOMETRIC APPROACH | ITO EQUATION | LIE SYMMETRIES | SYSTEMS | A generalized (3+1)-dimensional Kadomtsev-Petviashvili equation | RATIONAL CHARACTERISTICS | Water waves | Fluid dynamics

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 10/2016, Volume 60, pp. 96 - 100

Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the...

[formula omitted]-dimensional generalized variable-coefficient B-type Kadomtsev–Petviashvili equation | Fluids | Soliton solutions | Bell polynomials | Bäcklund transformation | (3+1)-dimensional generalized variable-coefficient B-type Kadomtsev-Petviashvili equation | MATHEMATICS, APPLIED | BREATHERS | Kadomtsev-Petviashvili equation | Backlund transformation | (3+1)-dimensional generalized variable-coefficient B-type | ROGUE WAVES | Fluid dynamics

[formula omitted]-dimensional generalized variable-coefficient B-type Kadomtsev–Petviashvili equation | Fluids | Soliton solutions | Bell polynomials | Bäcklund transformation | (3+1)-dimensional generalized variable-coefficient B-type Kadomtsev-Petviashvili equation | MATHEMATICS, APPLIED | BREATHERS | Kadomtsev-Petviashvili equation | Backlund transformation | (3+1)-dimensional generalized variable-coefficient B-type | ROGUE WAVES | Fluid dynamics

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 05/2016, Volume 71, Issue 10, pp. 2060 - 2068

Evolution of the long water waves and small-amplitude surface waves with the weak nonlinearity, weak dispersion and weak perturbation in fluid mechanics in...

Fluid mechanics | Generalized ([formula omitted])-dimensional variable-coefficient Kadomtsev–Petviashvili equation | Rouge waves | Homoclinic breather waves | Auto-Bäcklund transformation | Solitons | Generalized (3+1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation | Generalized (3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation | FERROMAGNETIC SPIN CHAIN | MATHEMATICS, APPLIED | PAINLEVE PROPERTY | Auto-Backlund transformation | NONLINEAR SCHRODINGER-EQUATION | Water waves | Analysis | Wave propagation | Perturbation methods | Mathematical analysis | Evolution | Mathematical models | Transformations | Stands

Fluid mechanics | Generalized ([formula omitted])-dimensional variable-coefficient Kadomtsev–Petviashvili equation | Rouge waves | Homoclinic breather waves | Auto-Bäcklund transformation | Solitons | Generalized (3+1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation | Generalized (3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation | FERROMAGNETIC SPIN CHAIN | MATHEMATICS, APPLIED | PAINLEVE PROPERTY | Auto-Backlund transformation | NONLINEAR SCHRODINGER-EQUATION | Water waves | Analysis | Wave propagation | Perturbation methods | Mathematical analysis | Evolution | Mathematical models | Transformations | Stands

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 10/2017, Volume 72, pp. 58 - 64

Under investigation in this work is a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation, which can describe many nonlinear phenomena in fluid...

Rogue waves | A generalized ([formula omitted])-dimensional Kadomtsev– Petviashvili equation | Breather waves | Bilinear form | Solitary waves | A generalized (3+1)-dimensional Kadomtsev– Petviashvili equation | Kadomtsev- Petviashvili equation | SYSTEM | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | INTEGRABILITY | A generalized (3+1)-dimensional | BREATHERS | SCHRODINGER | RATIONAL CHARACTERISTICS | Water waves | Fluid dynamics

Rogue waves | A generalized ([formula omitted])-dimensional Kadomtsev– Petviashvili equation | Breather waves | Bilinear form | Solitary waves | A generalized (3+1)-dimensional Kadomtsev– Petviashvili equation | Kadomtsev- Petviashvili equation | SYSTEM | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | INTEGRABILITY | A generalized (3+1)-dimensional | BREATHERS | SCHRODINGER | RATIONAL CHARACTERISTICS | Water waves | Fluid dynamics

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 06/2018, Volume 75, Issue 12, pp. 4221 - 4231

In this paper, a (3+1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation is investigated, which describes the dynamics of nonlinear waves in plasma...

Rogue wave solution | Breather wave solution | Dark soliton solution | The [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation | Bright soliton solution | Exact solution | The (3+1)-dimensional generalized Kadomtsev–Petviashvili equation | Water waves | Fluid dynamics | Plasma physics

Rogue wave solution | Breather wave solution | Dark soliton solution | The [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation | Bright soliton solution | Exact solution | The (3+1)-dimensional generalized Kadomtsev–Petviashvili equation | Water waves | Fluid dynamics | Plasma physics

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 06/2019, Volume 77, Issue 12, pp. 3154 - 3171

In this paper, under investigated is a generalized (3+1)-dimensional Camassa–Holm–Kadomtsev–Petviashvili (gCH-KP) equation, which describes the role of...

Conservation laws | Lie symmetries analysis | [formula omitted]-dimensional time fractional gCH-KP equation | Hirota bilinear method | RBF meshless approach | (3+1)-dimensional time fractional gCH-KP equation | MATHEMATICS, APPLIED | LUMP-KINK SOLUTIONS | FORMULATION | COMPACT | SOLITARY WAVES | FLUID | PARTIAL-DIFFERENTIAL-EQUATIONS | PEAKONS | GORDON | Finite element method | Radial basis function | Basis functions | Meshless methods | Euler-Lagrange equation | Drops (liquids) | Symmetry | Inverse method

Conservation laws | Lie symmetries analysis | [formula omitted]-dimensional time fractional gCH-KP equation | Hirota bilinear method | RBF meshless approach | (3+1)-dimensional time fractional gCH-KP equation | MATHEMATICS, APPLIED | LUMP-KINK SOLUTIONS | FORMULATION | COMPACT | SOLITARY WAVES | FLUID | PARTIAL-DIFFERENTIAL-EQUATIONS | PEAKONS | GORDON | Finite element method | Radial basis function | Basis functions | Meshless methods | Euler-Lagrange equation | Drops (liquids) | Symmetry | Inverse method

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 07/2019, Volume 78, Issue 1, pp. 166 - 177

Fluids are seen in a wide range of disciplines, including mechanical, civil, chemical and biomedical engineering, geophysics, astrophysics and biology. In this...

Hirota method | Lump wave–soliton interactions | Dark lump waves | [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation | Dark breather waves | Fluid | (3+1)-dimensional generalized Kadomtsev–Petviashvili equation | Water waves | Wave propagation | Analysis | Biomedical engineering | Organic chemistry | Amplitudes | Surface waves | Astrophysics | Geophysics | Nonlinearity | Perturbation | Fission

Hirota method | Lump wave–soliton interactions | Dark lump waves | [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation | Dark breather waves | Fluid | (3+1)-dimensional generalized Kadomtsev–Petviashvili equation | Water waves | Wave propagation | Analysis | Biomedical engineering | Organic chemistry | Amplitudes | Surface waves | Astrophysics | Geophysics | Nonlinearity | Perturbation | Fission

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 06/2013, Volume 26, Issue 6, pp. 612 - 616

In this paper, a (3+1)-dimensional generalized Kadomtsev–Petviashvili (KP) equation is first discussed using the pfaffianization procedure. A (3+1)-dimensional...

Pfaffianization | [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation | Gramm-type pfaffian | Wronski-type pfaffian | (3 + 1) -dimensional generalized Kadomtsev-Petviashvili equation | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | TERMS | DETERMINANT | ORDER ITO EQUATION | (3+1)-dimensional generalized Kadomtsev-Petviashvili equation | BACKLUND TRANSFORMATION | WATER-WAVES | EVOLUTION | HIERARCHIES | N-SOLITON SOLUTION | KORTEWEG-DEVRIES

Pfaffianization | [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation | Gramm-type pfaffian | Wronski-type pfaffian | (3 + 1) -dimensional generalized Kadomtsev-Petviashvili equation | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | TERMS | DETERMINANT | ORDER ITO EQUATION | (3+1)-dimensional generalized Kadomtsev-Petviashvili equation | BACKLUND TRANSFORMATION | WATER-WAVES | EVOLUTION | HIERARCHIES | N-SOLITON SOLUTION | KORTEWEG-DEVRIES

Journal Article

Physics Letters A, ISSN 0375-9601, 2007, Volume 366, Issue 4, pp. 411 - 421

In this Letter, Boussinesq–Burgers equation and ( 3 + 1 )-dimensional Kadomtsev–Petviashvili equation are studied by using a generalized algebraic method. A...

Boussinesq–Burgers equation | ( [formula omitted])-dimensional Kadomtsev–Petviashvili equation | Generalized algebraic method | Explicit exact travelling wave solutions | Boussinesq-Burgers equation | (3 + 1)-dimensional Kadomtsev-Petviashvili equation | EXPANSION METHOD | SERIES | PHYSICS, MULTIDISCIPLINARY | EVOLUTION-EQUATIONS | BACKLUND TRANSFORMATION | (3+1)-dimensional Kadomtsev-Petviashvili equation | JACOBI ELLIPTIC FUNCTION | INVERSE METHOD | VARIABLE-COEFFICIENTS | SOLITON-SOLUTIONS | KP EQUATION | generalized algebraic method | ALGEBRAIC-METHOD | explicit exact travelling wave solutions

Boussinesq–Burgers equation | ( [formula omitted])-dimensional Kadomtsev–Petviashvili equation | Generalized algebraic method | Explicit exact travelling wave solutions | Boussinesq-Burgers equation | (3 + 1)-dimensional Kadomtsev-Petviashvili equation | EXPANSION METHOD | SERIES | PHYSICS, MULTIDISCIPLINARY | EVOLUTION-EQUATIONS | BACKLUND TRANSFORMATION | (3+1)-dimensional Kadomtsev-Petviashvili equation | JACOBI ELLIPTIC FUNCTION | INVERSE METHOD | VARIABLE-COEFFICIENTS | SOLITON-SOLUTIONS | KP EQUATION | generalized algebraic method | ALGEBRAIC-METHOD | explicit exact travelling wave solutions

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 06/2018, Volume 75, Issue 12, pp. 4534 - 4539

In this paper, the (3+1)-dimensional generalized shallow water wave equation is investigated using the Hirota bilinear method and Kadomtsev–Petviashvili...

Kadomtsev–Petviashvili hierarchy reduction | Rational solutions | [formula omitted]-dimensional generalized shallow water wave equation | Lump soliton | (3+1)-dimensional generalized shallow water wave equation | MATHEMATICS, APPLIED | SOLITONS | LUMP-KINK SOLUTIONS | DYNAMICS | JIMBO-MIWA | KADOMTSEV-PETVIASHVILI EQUATION | Kadomtsev-Petviashvili hierarchy reduction | ORBITAL STABILITY | ROGUE WAVES | Information science

Kadomtsev–Petviashvili hierarchy reduction | Rational solutions | [formula omitted]-dimensional generalized shallow water wave equation | Lump soliton | (3+1)-dimensional generalized shallow water wave equation | MATHEMATICS, APPLIED | SOLITONS | LUMP-KINK SOLUTIONS | DYNAMICS | JIMBO-MIWA | KADOMTSEV-PETVIASHVILI EQUATION | Kadomtsev-Petviashvili hierarchy reduction | ORBITAL STABILITY | ROGUE WAVES | Information science

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2010, Volume 216, Issue 9, pp. 2771 - 2777

The G ′ G -expansion method can be used for constructing exact travelling wave solutions of real nonlinear evolution equations. In this paper, we improve the G...

[formula omitted]-expansion method | Exact complex travelling wave solutions | (2+1)-dimensional BKP equation | G))-expansion method | fenced(frac(G | (G '/G)-expansion method | MATHEMATICS, APPLIED | SOLITONS | MKDV | GENERALIZED (G'/G)-EXPANSION METHOD | NONLINEAR EVOLUTION-EQUATIONS | VARIANT BOUSSINESQ EQUATIONS | TANH-FUNCTION METHOD | KLEIN-GORDON EQUATIONS | Construction | Computation | Mathematical analysis | Exact solutions | Nonlinear evolution equations | Traveling waves | Mathematical models

[formula omitted]-expansion method | Exact complex travelling wave solutions | (2+1)-dimensional BKP equation | G))-expansion method | fenced(frac(G | (G '/G)-expansion method | MATHEMATICS, APPLIED | SOLITONS | MKDV | GENERALIZED (G'/G)-EXPANSION METHOD | NONLINEAR EVOLUTION-EQUATIONS | VARIANT BOUSSINESQ EQUATIONS | TANH-FUNCTION METHOD | KLEIN-GORDON EQUATIONS | Construction | Computation | Mathematical analysis | Exact solutions | Nonlinear evolution equations | Traveling waves | Mathematical models

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 229, Issue 1, pp. 158 - 167

In this letter, the Kaup–Kupershmidt, ( 2 + 1 ) -dimensional Potential Kadomtsev–Petviashvili (shortly PKP) equations are presented and the Exp-function method...

[formula omitted]-dimensional Potential Kadomtsev–Petviashvili (PKP) equation | Soliton | Kaup–Kupershmidt equation | Periodic solutions | Exp-function method | Traveling wave solution | (2 + 1)-dimensional Potential Kadomtsev-Petviashvili (PKP) equation | Kaup-Kupershmidt equation | SYSTEM | MATHEMATICS, APPLIED | HOMOTOPY PERTURBATION METHOD | 5TH-ORDER KDV EQUATIONS | KADOMTSEV-PETVIASHVILI EQUATION | (2+1)-dimensional Potential Kadomtsev-Petviashvili (PKP) equation | WAVE-EQUATIONS | LATTICE | Mechanical engineering | Methods

[formula omitted]-dimensional Potential Kadomtsev–Petviashvili (PKP) equation | Soliton | Kaup–Kupershmidt equation | Periodic solutions | Exp-function method | Traveling wave solution | (2 + 1)-dimensional Potential Kadomtsev-Petviashvili (PKP) equation | Kaup-Kupershmidt equation | SYSTEM | MATHEMATICS, APPLIED | HOMOTOPY PERTURBATION METHOD | 5TH-ORDER KDV EQUATIONS | KADOMTSEV-PETVIASHVILI EQUATION | (2+1)-dimensional Potential Kadomtsev-Petviashvili (PKP) equation | WAVE-EQUATIONS | LATTICE | Mechanical engineering | Methods

Journal Article

Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 20, pp. 3653 - 3658

In this Letter, the ( G ′ G ) -expansion method [M.L. Wang, X.Z. Li, J.L. Zhang, Phys. Lett. A 372 (2008) 417] is improved and a generalized ( G ′ G )...

Kadomstev–Petviashvili equation | Generalized [formula omitted]-expansion method | Nizhnik–Novikov–Vesselov equation | Broer–Kaup equation | Exact solutions | Nizhnik-Novikov-Vesselov equation | Generalized (frac(G | G))-expansion method | Kadomstev-Petviashvili equation | Broer-Kaup equation | MATHEMATICAL PHYSICS | PHYSICS, MULTIDISCIPLINARY | WAVE SOLUTIONS | generalized (G '/G)-expansion method | HOMOGENEOUS BALANCE METHOD | KADOMTSEV-PETVIASHVILI EQUATIONS | exact solutions | SOLITON-SOLUTIONS | WRONSKIAN TECHNIQUE | NONLINEAR EVOLUTION-EQUATIONS | KORTEWEG-DEVRIES

Kadomstev–Petviashvili equation | Generalized [formula omitted]-expansion method | Nizhnik–Novikov–Vesselov equation | Broer–Kaup equation | Exact solutions | Nizhnik-Novikov-Vesselov equation | Generalized (frac(G | G))-expansion method | Kadomstev-Petviashvili equation | Broer-Kaup equation | MATHEMATICAL PHYSICS | PHYSICS, MULTIDISCIPLINARY | WAVE SOLUTIONS | generalized (G '/G)-expansion method | HOMOGENEOUS BALANCE METHOD | KADOMTSEV-PETVIASHVILI EQUATIONS | exact solutions | SOLITON-SOLUTIONS | WRONSKIAN TECHNIQUE | NONLINEAR EVOLUTION-EQUATIONS | KORTEWEG-DEVRIES

Journal Article

Journal of Fluid Mechanics, ISSN 0022-1120, 06/2017, Volume 820, pp. 208 - 231

The formationof a singularity in a compressible gas, as described by the Luler equation, is characterized by the steepening and eventual overturning of a Wave....

Compressible flows | shock waves | MECHANICS | compressible flows | SINGULARITIES | PHYSICS, FLUIDS & PLASMAS | WAVE-BREAKING | KADOMTSEV-PETVIASHVILI EQUATION | EULER | Shock | Catastrophes | Compressibility | Partial differential equations | One dimensional models | Spatial discrimination | Dimensions | Hazards | Euler-Lagrange equation | Power series | Direction | Shock waves | Caustic lines | Kinematics | Series expansion | Mathematical models | Formulas (mathematics) | Lines | Self-similarity

Compressible flows | shock waves | MECHANICS | compressible flows | SINGULARITIES | PHYSICS, FLUIDS & PLASMAS | WAVE-BREAKING | KADOMTSEV-PETVIASHVILI EQUATION | EULER | Shock | Catastrophes | Compressibility | Partial differential equations | One dimensional models | Spatial discrimination | Dimensions | Hazards | Euler-Lagrange equation | Power series | Direction | Shock waves | Caustic lines | Kinematics | Series expansion | Mathematical models | Formulas (mathematics) | Lines | Self-similarity

Journal Article

Physics Letters A, ISSN 0375-9601, 2004, Volume 330, Issue 6, pp. 448 - 459

Symmetry constraints for ( 2 + 1 ) -dimensional dispersionless integrable equations are considered. It is demonstrated that they naturally lead to certain...

Dispersionless integrable hierarchies | Symmetry constraints | Systems of hydrodynamic type | Quasiclassical [formula omitted]-method | method | Quasiclassical | BENNEY EQUATIONS | WHITHAM HIERARCHY | HODOGRAPH SOLUTIONS | MOMENT EQUATIONS | CONFORMAL-MAPS | PHYSICS, MULTIDISCIPLINARY | KP HIERARCHY | TAU-FUNCTION | TOPOLOGICAL FIELD-THEORY | KORTEWEG-DEVRIES EQUATION | KADOMTSEV-PETVIASHVILI | symmetry constraints | quasiclassical partial derivative-method | dispersionless integrable hierarchies | systems of hydrodynamic type | Physics - Exactly Solvable and Integrable Systems

Dispersionless integrable hierarchies | Symmetry constraints | Systems of hydrodynamic type | Quasiclassical [formula omitted]-method | method | Quasiclassical | BENNEY EQUATIONS | WHITHAM HIERARCHY | HODOGRAPH SOLUTIONS | MOMENT EQUATIONS | CONFORMAL-MAPS | PHYSICS, MULTIDISCIPLINARY | KP HIERARCHY | TAU-FUNCTION | TOPOLOGICAL FIELD-THEORY | KORTEWEG-DEVRIES EQUATION | KADOMTSEV-PETVIASHVILI | symmetry constraints | quasiclassical partial derivative-method | dispersionless integrable hierarchies | systems of hydrodynamic type | Physics - Exactly Solvable and Integrable Systems

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 04/2020, Volume 102, p. 106145

In this paper, multiple rogue wave solutions of a generalized (3+1)-dimensional Kadomtsev–Petviashvili (KP) equation are studied. Based on the bilinear form of...

Generalized (3+1)-dimensional KP equation | Bilinear form | [formula omitted]-rogue waves

Generalized (3+1)-dimensional KP equation | Bilinear form | [formula omitted]-rogue waves

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 02/2010, Volume 15, Issue 2, pp. 216 - 224

In this paper, the extended tanh method, the sech–csch ansatz, the Hirota’s bilinear formalism combined with the simplified Hereman form and the Darboux...

Complexitons | Travelling wave solutions | [formula omitted]-Dimensional KD equation | (2 + 1)-Dimensional KD equation | TRANSFORMATION | MATHEMATICAL PHYSICS | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | TANH METHOD | PHYSICS, FLUIDS & PLASMAS | SOLITONS SOLUTIONS | (2+1)-Dimensional KD equation | SYMBOLIC-COMPUTATION | PHYSICS, MATHEMATICAL | COMPLEXITON SOLUTIONS | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EXPANSION | NONLINEAR EVOLUTION-EQUATIONS

Complexitons | Travelling wave solutions | [formula omitted]-Dimensional KD equation | (2 + 1)-Dimensional KD equation | TRANSFORMATION | MATHEMATICAL PHYSICS | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | TANH METHOD | PHYSICS, FLUIDS & PLASMAS | SOLITONS SOLUTIONS | (2+1)-Dimensional KD equation | SYMBOLIC-COMPUTATION | PHYSICS, MATHEMATICAL | COMPLEXITON SOLUTIONS | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EXPANSION | NONLINEAR EVOLUTION-EQUATIONS

Journal Article

Science China Mathematics, ISSN 1674-7283, 2/2015, Volume 58, Issue 2, pp. 279 - 296

We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear method. This approach is mainly based on the...

37J35 | Bäcklund transformation | integrable discretization | Mathematics | Applications of Mathematics | bilinear method | 37K10 | Bilinear method | Integrable discretization | NONLINEAR SUPERPOSITION FORMULAS | MATHEMATICS | MATHEMATICS, APPLIED | KDV EQUATION | Backlund transformation | EVOLUTION-EQUATIONS | PARTIAL DIFFERENCE-EQUATIONS | Computer science | Methods

37J35 | Bäcklund transformation | integrable discretization | Mathematics | Applications of Mathematics | bilinear method | 37K10 | Bilinear method | Integrable discretization | NONLINEAR SUPERPOSITION FORMULAS | MATHEMATICS | MATHEMATICS, APPLIED | KDV EQUATION | Backlund transformation | EVOLUTION-EQUATIONS | PARTIAL DIFFERENCE-EQUATIONS | Computer science | Methods

Journal Article