Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 08/2019, Volume 528, p. 121320

Solutions of the nonlinear physical problems are significant and a vital topic in real life while the soliton based algorithms are promising techniques to...

Kadomtsev–Petviashvili (KP) equations | Soliton solutions | Fractional calculus | Multiple exp-function method | HIGHER-ORDER | PHYSICS, MULTIDISCIPLINARY | DIFFERENTIAL-EQUATIONS | WAVE SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | Kadomtsev-Petviashvili (KP) equations

Kadomtsev–Petviashvili (KP) equations | Soliton solutions | Fractional calculus | Multiple exp-function method | HIGHER-ORDER | PHYSICS, MULTIDISCIPLINARY | DIFFERENTIAL-EQUATIONS | WAVE SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | Kadomtsev-Petviashvili (KP) equations

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 11/2017, Volume 74, Issue 10, pp. 2599 - 2607

The aim of this paper is to obtain the exact solutions with the help of similarity transformations method for Kadomtsev–Petviashvili (KP) equation in...

Similarity solutions | KP equation | Similarity transformations method | Lie-group | Solitons | REDUCTIONS | SYSTEM | WAVE | MATHEMATICS, APPLIED | SYMMETRIES | HIERARCHY | Usage | Differential equations

Similarity solutions | KP equation | Similarity transformations method | Lie-group | Solitons | REDUCTIONS | SYSTEM | WAVE | MATHEMATICS, APPLIED | SYMMETRIES | HIERARCHY | Usage | Differential equations

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2015, Volume 299, pp. 716 - 730

We consider a splitting approach for the Kadomtsev–Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure...

Dispersive equation | Kadomtsev–Petviashvili equation | Splitting methods | Kadomtsev-Petviashvili equation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MASS CONSTRAINT | PHYSICS, MATHEMATICAL | Extrapolation | Interpolation | Order reduction | Splitting | Mathematical analysis | Conservation | Boundary conditions | Mathematical models

Dispersive equation | Kadomtsev–Petviashvili equation | Splitting methods | Kadomtsev-Petviashvili equation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MASS CONSTRAINT | PHYSICS, MATHEMATICAL | Extrapolation | Interpolation | Order reduction | Splitting | Mathematical analysis | Conservation | Boundary conditions | Mathematical models

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 11/2016, Volume 72, Issue 9, pp. 2072 - 2083

In this paper, we use a new direct method namely modified (w/g )- expansion method to obtain the exact solutions for the integral members of nonlinear...

Integral members of nonlinear KPH equations | Modified(w/g)- expansion method | Exact solutions | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | F-EXPANSION | TANH-FUNCTION | BURGERS | SOLITON-SOLUTIONS | HOMOTOPY PERTURBATION METHOD | Methods | Differential equations | Hierarchies | Integrals | Mathematical analysis | Nonlinearity | Mathematical models | Solitary waves

Integral members of nonlinear KPH equations | Modified(w/g)- expansion method | Exact solutions | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | F-EXPANSION | TANH-FUNCTION | BURGERS | SOLITON-SOLUTIONS | HOMOTOPY PERTURBATION METHOD | Methods | Differential equations | Hierarchies | Integrals | Mathematical analysis | Nonlinearity | Mathematical models | Solitary waves

Journal Article

5.
Full Text
A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev–Petviashvili equation

Applied Mathematics and Computation, ISSN 0096-3003, 10/2018, Volume 334, pp. 311 - 325

In this paper we propose a method to solve the Kadomtsev–Petviashvili equation based on splitting the linear part of the equation from the nonlinear part. The...

method of characteristics | semi-Lagrangian discontinuous Galerkin methods | KP equation | time splitting | MATHEMATICS, APPLIED | WAVES | EVOLUTION | Analysis | Numerical analysis

method of characteristics | semi-Lagrangian discontinuous Galerkin methods | KP equation | time splitting | MATHEMATICS, APPLIED | WAVES | EVOLUTION | Analysis | Numerical analysis

Journal Article

Modern Physics Letters B, ISSN 0217-9849, 04/2019, Volume 33, Issue 10, p. 1950126

A new generalized Kadomtsev–Petviashvili (GKP) equation is derived from a bilinear differential equation by taking the transformation u = 2 ( ln f ) x . By...

Hirota bilinear form | GKP equation | Lump solution | RATIONAL SOLUTIONS | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | ALGORITHMIC CONSTRUCTION | PHYSICS, MATHEMATICAL | BACKLUND TRANSFORMATION

Hirota bilinear form | GKP equation | Lump solution | RATIONAL SOLUTIONS | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | ALGORITHMIC CONSTRUCTION | PHYSICS, MATHEMATICAL | BACKLUND TRANSFORMATION

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 12/2014, Volume 332, Issue 2, pp. 505 - 533

We study the large time asymptotic behavior of solutions to the Kadomtsev–Petviashvili equations $$\left\{\begin{array}{ll} u_{t} + u_{xxx} + \sigma...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | PHYSICS, MATHEMATICAL

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | PHYSICS, MATHEMATICAL

Journal Article

Computers & Mathematics with Applications, ISSN 0898-1221, 11/2017, Volume 74, Issue 10, p. 2599

The aim of this paper is to obtain the exact solutions with the help of similarity transformations method for Kadomtsev-Petviashvili (KP) equation in...

Studies | Boussinesq equations | Similarity | Differential equations | Ordinary differential equations | Constants | Transformations | Solitary waves

Studies | Boussinesq equations | Similarity | Differential equations | Ordinary differential equations | Constants | Transformations | Solitary waves

Journal Article

Communications in Theoretical Physics, ISSN 0253-6102, 08/2016, Volume 66, Issue 2, pp. 189 - 195

A generalized Kadomtsev-Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion (CRE) method in this paper. Applying the...

consistent riccati expansion | Painlevé expansion | soliton-cnoidal wave solution | nonlocal symmetry | Painleve expansion | INTEGRABLE MODELS | REDUCTION | PHYSICS, MULTIDISCIPLINARY | PARTIAL-DIFFERENTIAL-EQUATIONS | KDV EQUATION | PAINLEVE PROPERTY | TRANSFORMATIONS | WATER-WAVE SYSTEM | Transformations | Wave interaction | Theoretical physics | Mathematical analysis | Symmetry

consistent riccati expansion | Painlevé expansion | soliton-cnoidal wave solution | nonlocal symmetry | Painleve expansion | INTEGRABLE MODELS | REDUCTION | PHYSICS, MULTIDISCIPLINARY | PARTIAL-DIFFERENTIAL-EQUATIONS | KDV EQUATION | PAINLEVE PROPERTY | TRANSFORMATIONS | WATER-WAVE SYSTEM | Transformations | Wave interaction | Theoretical physics | Mathematical analysis | Symmetry

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 8/2018, Volume 196, Issue 2, pp. 1174 - 1199

We construct solutions of the Kadomtsev–Petviashvili-I equation in terms of Fredholm determinants. We deduce solutions written as a quotient of Wronskians of...

Wronskian | Theoretical, Mathematical and Computational Physics | rogue wave | Applications of Mathematics | Kadomtsev–Petviashvili equation | Physics | lump | Fredholm determinant | PHYSICS, MULTIDISCIPLINARY | Kadomtsev-Petviashvili equation | PHYSICS, MATHEMATICAL | NONSTATIONARY SCHRODINGER | LUMPS | SYSTEMS | N-SOLITON SOLUTIONS | WRONSKIAN FORM | HIERARCHY | Water waves

Wronskian | Theoretical, Mathematical and Computational Physics | rogue wave | Applications of Mathematics | Kadomtsev–Petviashvili equation | Physics | lump | Fredholm determinant | PHYSICS, MULTIDISCIPLINARY | Kadomtsev-Petviashvili equation | PHYSICS, MATHEMATICAL | NONSTATIONARY SCHRODINGER | LUMPS | SYSTEMS | N-SOLITON SOLUTIONS | WRONSKIAN FORM | HIERARCHY | Water waves

Journal Article

中国物理B：英文版, ISSN 1674-1056, 2014, Volume 23, Issue 10, pp. 1 - 6

The residual symmetry relating to the truncated Painlev6 expansion of the Kadomtsev-Petviashvili （KP） equation is nonlocal, which is localized in this paper by...

一般形式 | 李群方法 | 相互作用 | KP方程 | 交互 | 对称性 | 时间系统 | 使用标准 | Kadomtsev-Petviashvili equation | symmetry reduction solution | localization procedure | residual symmetry | Bäcklund transformation | SOLITON HIERARCHY | PHYSICS, MULTIDISCIPLINARY | Backlund transformation | NONLOCAL SYMMETRIES | Reduction | Dependent variables | Mathematical analysis | Lie groups | Solitons | Standards | Symmetry | Physics - Exactly Solvable and Integrable Systems

一般形式 | 李群方法 | 相互作用 | KP方程 | 交互 | 对称性 | 时间系统 | 使用标准 | Kadomtsev-Petviashvili equation | symmetry reduction solution | localization procedure | residual symmetry | Bäcklund transformation | SOLITON HIERARCHY | PHYSICS, MULTIDISCIPLINARY | Backlund transformation | NONLOCAL SYMMETRIES | Reduction | Dependent variables | Mathematical analysis | Lie groups | Solitons | Standards | Symmetry | Physics - Exactly Solvable and Integrable Systems

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 11/2017, Volume 263, Issue 9, pp. 5696 - 5726

The Cauchy problem of the fifth order Kadomtsev–Petviashvili-I equation (fifth-KP-I)(0.1)∂tu+∂x5u±∂x3u−∂x−1∂yyu+∂x(u2)=0,(x,y,t)∈R3; is considered. It follows...

Dyadic [formula omitted] spaces | Fifth order Kadomtsev–Petviashvili-I equation | Well-posedness | Dyadic X | spaces | MATHEMATICS | SOBOLEV SPACES | Fifth order Kadomtsev-Petviashvili-I equation | Dyadic X-s,X-b spaces | CAUCHY-PROBLEM | GLOBAL WELL-POSEDNESS

Dyadic [formula omitted] spaces | Fifth order Kadomtsev–Petviashvili-I equation | Well-posedness | Dyadic X | spaces | MATHEMATICS | SOBOLEV SPACES | Fifth order Kadomtsev-Petviashvili-I equation | Dyadic X-s,X-b spaces | CAUCHY-PROBLEM | GLOBAL WELL-POSEDNESS

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 12/2013, Volume 265, pp. 1 - 25

The formation of singularities in solutions to the dispersionless Kadomtsev–Petviashvili (dKP) equation is studied numerically for different classes of initial...

Burgers equation | Dispersive shocks | Kadomtsev–Petviashvili equation | Asymptotic Fourier analysis | Korteweg–de Vries equation | Asymptotic | Fourier analysis | Vries equation | Kadomtsev-Petviashvili equation | Korteweg-de | COMPLEX SINGULARITIES | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | CAUCHY-PROBLEM | LIMIT | PHYSICS, MATHEMATICAL | Korteweg-de Vries equation | DYNAMICS | EULER FLOW | SYSTEMS

Burgers equation | Dispersive shocks | Kadomtsev–Petviashvili equation | Asymptotic Fourier analysis | Korteweg–de Vries equation | Asymptotic | Fourier analysis | Vries equation | Kadomtsev-Petviashvili equation | Korteweg-de | COMPLEX SINGULARITIES | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | CAUCHY-PROBLEM | LIMIT | PHYSICS, MATHEMATICAL | Korteweg-de Vries equation | DYNAMICS | EULER FLOW | SYSTEMS

Journal Article

Wave Motion, ISSN 0165-2125, 03/2018, Volume 77, pp. 243 - 256

The interactions of multi-lumps within the Kadomtsev–Petviashvili-1 (KP1) equation are studied analytically and numerically. The dependence of stationary...

Hirota transformation | Soliton interaction | Kadomtsev–Petviashvili equation | Lump solution | GRAVITY-CAPILLARY LUMPS | PHYSICS, MULTIDISCIPLINARY | BOTTOM TOPOGRAPHY | Kadomtsev-Petviashvili equation | ACOUSTICS | WAVES | MECHANICS | I EQUATION | SOLITONS | EVOLUTION | GENERATION | PLATE

Hirota transformation | Soliton interaction | Kadomtsev–Petviashvili equation | Lump solution | GRAVITY-CAPILLARY LUMPS | PHYSICS, MULTIDISCIPLINARY | BOTTOM TOPOGRAPHY | Kadomtsev-Petviashvili equation | ACOUSTICS | WAVES | MECHANICS | I EQUATION | SOLITONS | EVOLUTION | GENERATION | PLATE

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 8/2018, Volume 196, Issue 2, pp. 1164 - 1173

In the tropical limit of matrix KP-II solitons, their support at a fixed time is a planar graph with “polarizations” attached to its linear parts. We explore a...

Yang–Baxter map | binary tree | soliton | hexagon equation | Theoretical, Mathematical and Computational Physics | dilogarithm | pentagon equation | Applications of Mathematics | KP equation | tropical limit | Physics | PHYSICS, MULTIDISCIPLINARY | Yang-Baxter map | PHYSICS, MATHEMATICAL

Yang–Baxter map | binary tree | soliton | hexagon equation | Theoretical, Mathematical and Computational Physics | dilogarithm | pentagon equation | Applications of Mathematics | KP equation | tropical limit | Physics | PHYSICS, MULTIDISCIPLINARY | Yang-Baxter map | PHYSICS, MATHEMATICAL

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 1, pp. 156 - 181

In this paper we study special properties of solutions of the initial value problem (IVP) associated to the fifth order Kadomtsev-Petviashvili II equation....

Local well-posedness | Fifth order Kadomtsev-Petviashvili II equation | Propagation of regularity | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | SOLITARY WAVES | Fifth order Kadomtsev-Petviashvili | CAUCHY-PROBLEM | II equation | GLOBAL WELL-POSEDNESS

Local well-posedness | Fifth order Kadomtsev-Petviashvili II equation | Propagation of regularity | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | SOLITARY WAVES | Fifth order Kadomtsev-Petviashvili | CAUCHY-PROBLEM | II equation | GLOBAL WELL-POSEDNESS

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 04/2015, Volume 300, pp. 1 - 14

A wealth of observations, recently supported by rigorous analysis, indicate that, asymptotically in time, most multi-soliton solutions of the...

KP II equation | Soliton webs | Junction “lattice” | Junction "lattice" | TOTAL POSITIVITY | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | KP EQUATION | PHYSICS, FLUIDS & PLASMAS | HIERARCHIES | POTENTIALS | PHYSICS, MATHEMATICAL | TRANSFORMATION GROUPS

KP II equation | Soliton webs | Junction “lattice” | Junction "lattice" | TOTAL POSITIVITY | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | KP EQUATION | PHYSICS, FLUIDS & PLASMAS | HIERARCHIES | POTENTIALS | PHYSICS, MATHEMATICAL | TRANSFORMATION GROUPS

Journal Article

Physica Scripta, ISSN 0031-8949, 02/2013, Volume 87, Issue 2, pp. 25003 - 12

In this paper, we study the Kadomtsev-Petviashvili equation with generalized evolution and derive some new results using the approach called the trial equation...

TRAVELING-WAVE SOLUTIONS | CAMASSA-HOLM | PHYSICS, MULTIDISCIPLINARY | NONLINEAR EVOLUTION-EQUATIONS | Mathematical analysis | Rational functions | Classification | Exact solutions | Differential equations | Nonlinearity | Evolution | Elliptic functions

TRAVELING-WAVE SOLUTIONS | CAMASSA-HOLM | PHYSICS, MULTIDISCIPLINARY | NONLINEAR EVOLUTION-EQUATIONS | Mathematical analysis | Rational functions | Classification | Exact solutions | Differential equations | Nonlinearity | Evolution | Elliptic functions

Journal Article

理论物理通讯：英文版, ISSN 0253-6102, 2016, Volume 65, Issue 3, pp. 341 - 346

The nonlocal symmetry for the potential Kadomtsev-Petviashvili（pKP） equation is derived by the truncated Painleve analysis.The nonlocal symmetry is localized...

对称变换 | 局域对称性 | 相互作用 | 非局部 | 辅助变量 | Backlund变换 | KP方程 | 函数展开法 | SOLITON-LIKE SOLUTIONS | P-POWER | consistent tanh expansion method | potential Kadomtsev-Petviashvili equation | PHYSICS, MULTIDISCIPLINARY | front wave | BURGERS-EQUATION | WAVE SOLUTIONS | nonlocal symmetry | Construction | Theorems | Dependent variables | Existence theorems | Mathematical analysis | Transformations | Localization | Symmetry

对称变换 | 局域对称性 | 相互作用 | 非局部 | 辅助变量 | Backlund变换 | KP方程 | 函数展开法 | SOLITON-LIKE SOLUTIONS | P-POWER | consistent tanh expansion method | potential Kadomtsev-Petviashvili equation | PHYSICS, MULTIDISCIPLINARY | front wave | BURGERS-EQUATION | WAVE SOLUTIONS | nonlocal symmetry | Construction | Theorems | Dependent variables | Existence theorems | Mathematical analysis | Transformations | Localization | Symmetry

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 05/2016, Volume 34, pp. 210 - 223

•By means of the gauge transformation, the Wronskian solutions of the DNLS equations have been given.•We have got the bright soliton and the dark-bright...

Gauge transformation | Constrained discrete KP hierarchy | Wronskian solution | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | KP HIERARCHY | GAUGE TRANSFORMATIONS | EQUATIONS | PHYSICS, MATHEMATICAL | ADDITIONAL SYMMETRIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | DETERMINANT REPRESENTATION | OPERATORS

Gauge transformation | Constrained discrete KP hierarchy | Wronskian solution | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | KP HIERARCHY | GAUGE TRANSFORMATIONS | EQUATIONS | PHYSICS, MATHEMATICAL | ADDITIONAL SYMMETRIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | DETERMINANT REPRESENTATION | OPERATORS

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.