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 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

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

4.
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

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

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

Journal of Nonlinear Science, ISSN 0938-8974, 10/2012, Volume 22, Issue 5, pp. 763 - 811

We first review the known mathematical results concerning the Kadomtsev–Petviashvili type equations. Then we perform numerical simulations to analyze various...

Stability | 35B35 | Theoretical, Mathematical and Computational Physics | Mathematics | Qualitative properties | 35Q53 | 37K10 | Blow-up | Kadomtsev–Petviashvili equations | Analysis | Appl.Mathematics/Computational Methods of Engineering | Mechanics | Economic Theory | 35B40 | Kadomtsev-Petviashvili equations | MATHEMATICS, APPLIED | INVERSE SCATTERING TRANSFORM | KP-II EQUATION | CAUCHY-PROBLEM | PHYSICS, MATHEMATICAL | GLOBAL WELL-POSEDNESS | SOBOLEV SPACES | MECHANICS | LONG WAVES | SOLITARY WAVES | PERIODIC TRAVELING-WAVES | 2-DIMENSIONAL SOLITONS | TRANSVERSE INSTABILITY

Stability | 35B35 | Theoretical, Mathematical and Computational Physics | Mathematics | Qualitative properties | 35Q53 | 37K10 | Blow-up | Kadomtsev–Petviashvili equations | Analysis | Appl.Mathematics/Computational Methods of Engineering | Mechanics | Economic Theory | 35B40 | Kadomtsev-Petviashvili equations | MATHEMATICS, APPLIED | INVERSE SCATTERING TRANSFORM | KP-II EQUATION | CAUCHY-PROBLEM | PHYSICS, MATHEMATICAL | GLOBAL WELL-POSEDNESS | SOBOLEV SPACES | MECHANICS | LONG WAVES | SOLITARY WAVES | PERIODIC TRAVELING-WAVES | 2-DIMENSIONAL SOLITONS | TRANSVERSE INSTABILITY

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2011, Volume 240, Issue 6, pp. 477 - 511

The KPII equation is an integrable nonlinear PDE in 2+1 dimensions (two spatial and one temporal), which arises in several physical circumstances, including...

[formula omitted]-bar | Spectral analysis | Integrable nonlinear PDE | MATHEMATICS, APPLIED | INVERSE SCATTERING | DAVEY-STEWARTSON | PHYSICS, MULTIDISCIPLINARY | PDES | BOUNDARY-VALUE-PROBLEMS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | KORTEWEG-DEVRIES EQUATION | GENERALIZED DIRICHLET | LINE | NEUMANN MAP | Integrable nonlinear POE | TRANSFORM | d-bar | Fluid mechanics | Boundary value problems | Mathematical analysis | Initial value problems | Boundaries | Formalism | Joints | Shallow water | Temporal logic

[formula omitted]-bar | Spectral analysis | Integrable nonlinear PDE | MATHEMATICS, APPLIED | INVERSE SCATTERING | DAVEY-STEWARTSON | PHYSICS, MULTIDISCIPLINARY | PDES | BOUNDARY-VALUE-PROBLEMS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | KORTEWEG-DEVRIES EQUATION | GENERALIZED DIRICHLET | LINE | NEUMANN MAP | Integrable nonlinear POE | TRANSFORM | d-bar | Fluid mechanics | Boundary value problems | Mathematical analysis | Initial value problems | Boundaries | Formalism | Joints | Shallow water | Temporal logic

Journal Article

Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 2014, Volume 19, Issue 6, pp. 1689 - 1717

We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized...

Generalized Kadomtsev-Petviasvili equations | Numerical approaches | Dynamic rescaling | Blow-up | numerical approaches | MATHEMATICS, APPLIED | MASS CONSTRAINT | SOLITARY WAVES | DECAY | blow-up | CAUCHY-PROBLEM | dynamic rescaling | KORTEWEG-DE-VRIES

Generalized Kadomtsev-Petviasvili equations | Numerical approaches | Dynamic rescaling | Blow-up | numerical approaches | MATHEMATICS, APPLIED | MASS CONSTRAINT | SOLITARY WAVES | DECAY | blow-up | CAUCHY-PROBLEM | dynamic rescaling | KORTEWEG-DE-VRIES

Journal Article

10.
On concentration of semi-classical solitary waves for a generalized kadomtsev-petviashvili equation

Discrete and Continuous Dynamical Systems - Series S, ISSN 1937-1632, 10/2017, Volume 10, Issue 5, pp. 1095 - 1106

The present paper is concerned with semi-classical solitary wave solutions of a generalized Kadomtsev-Petviashvili equation in R-2. Parameter epsilon and...

EXISTENCE | solitary wave | critical point | MATHEMATICS, APPLIED | STATES | Kadomtsev-Petviashvili equation | WELL-POSEDNESS | Concentration | semi-classical

EXISTENCE | solitary wave | critical point | MATHEMATICS, APPLIED | STATES | Kadomtsev-Petviashvili equation | WELL-POSEDNESS | Concentration | semi-classical

Journal Article

理论物理通讯：英文版, ISSN 0253-6102, 2014, Volume 61, Issue 3, pp. 339 - 343

Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable...

符号计算 | Wronski行列式 | KP方程 | 线性偏微分方程 | N-孤子解 | 广义变系数 | 表单 | 方程组 | multi-soliton-like solution | symbolic computatio | wronsian form solution | variable coefficient KP equation | PHYSICS, MULTIDISCIPLINARY | KP EQUATION | symbolic computation | SOLITON-LIKE | PAINLEVE PROPERTY

符号计算 | Wronski行列式 | KP方程 | 线性偏微分方程 | N-孤子解 | 广义变系数 | 表单 | 方程组 | multi-soliton-like solution | symbolic computatio | wronsian form solution | variable coefficient KP equation | PHYSICS, MULTIDISCIPLINARY | KP EQUATION | symbolic computation | SOLITON-LIKE | PAINLEVE PROPERTY

Journal Article

Communications in Theoretical Physics, ISSN 0253-6102, 04/2010, Volume 53, Issue 4, pp. 698 - 702

In this paper, the extended symmetry of generalized variable-coefficient Kadomtsev-Petviashvili (vcKP) equation is investigated by the extended symmetry group...

Generalized variable-coefficient KP equation | Extended symmetry | WATER-WAVES | INTEGRABILITY | PHYSICS, MULTIDISCIPLINARY | KP EQUATION | SIMILARITY REDUCTIONS | extended symmetry | generalized variable-coefficient KP equation | NONLINEAR SCHRODINGER-EQUATION | DEPTH

Generalized variable-coefficient KP equation | Extended symmetry | WATER-WAVES | INTEGRABILITY | PHYSICS, MULTIDISCIPLINARY | KP EQUATION | SIMILARITY REDUCTIONS | extended symmetry | generalized variable-coefficient KP equation | NONLINEAR SCHRODINGER-EQUATION | DEPTH

Journal Article

理论物理通讯：英文版, ISSN 0253-6102, 2016, Volume 65, Issue 8, pp. 189 - 195

Journal Article

02/2011

Physical Review A 81 (2010) 33824 By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili...

Physics - Optics

Physics - Optics

Journal Article

Canadian Journal of Physics, ISSN 0008-4204, 09/2011, Volume 89, Issue 9, pp. 979 - 984

This study obtained the shock wave or kink solutions of the variants of the Kadomtsev–Petviashvili equation with generalized evolution. There are three types...

02.30.Jr | 02.30.Ik | 52.35.Sb | 42.81.Dp | PHYSICS, MULTIDISCIPLINARY | KP EQUATION | Shock waves | Research | Derivation | Evolution | Mathematical analysis

02.30.Jr | 02.30.Ik | 52.35.Sb | 42.81.Dp | PHYSICS, MULTIDISCIPLINARY | KP EQUATION | Shock waves | Research | Derivation | Evolution | Mathematical analysis

Journal Article

Inverse Problems, ISSN 0266-5611, 08/2007, Volume 23, Issue 4, pp. 1433 - 1444

A new type of the KP equation with self- consistent sources (KPESCS) first found by Mel'nikov ( 1983 Lett. Math. Phys. 7 129-36) is re-constructed via source...

MATHEMATICS, APPLIED | MULTISOLITON SOLUTIONS | WAVES | KP EQUATION | CONSTRUCTION | HIERARCHIES | PHYSICS, MATHEMATICAL

MATHEMATICS, APPLIED | MULTISOLITON SOLUTIONS | WAVES | KP EQUATION | CONSTRUCTION | HIERARCHIES | PHYSICS, MATHEMATICAL

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2012, Volume 364, Issue 7, pp. 3395 - 3425

solutions and decay estimates of solitary waves to the rotation-modified Kadomtsev-Petviashvili (rmKP) equation. It is shown that with negative dispersion, the...

Integers | Mathematical theorems | Mathematical integrals | Solitons | Differential equations | Fourier transformations | High frequencies | Rotation | Cauchy problem | Solitary wave | Kadomtsev-Petviashvili | Well-posedness | MATHEMATICS | solitary wave | well-posedness | INTERNAL WAVES | rotation | KP-II EQUATION | GLOBAL WELL-POSEDNESS | SCATTERING

Integers | Mathematical theorems | Mathematical integrals | Solitons | Differential equations | Fourier transformations | High frequencies | Rotation | Cauchy problem | Solitary wave | Kadomtsev-Petviashvili | Well-posedness | MATHEMATICS | solitary wave | well-posedness | INTERNAL WAVES | rotation | KP-II EQUATION | GLOBAL WELL-POSEDNESS | SCATTERING

Journal Article

Astrophysics and Space Science, ISSN 0004-640X, 2/2014, Volume 349, Issue 2, pp. 813 - 820

For the critical values of the parameters q and V, the work (Samanta et al. in Phys. Plasma 20:022111, 2013b) is unable to describe the nonlinear wave features...

Solitary wave | Extraterrestrial Physics, Space Sciences | Dusty plasma | Astrophysics and Astroparticles | Astrobiology | Periodic wave | Kink and anti-kink waves | Cosmology | Physics | Astronomy, Observations and Techniques | ASTRONOMY & ASTROPHYSICS | NONEXTENSIVE STATISTICS | CRYSTALS | SOLAR-SYSTEM | SOLITON | Geomagnetism | Plasma physics | Wave propagation | Magnetosphere | Electrons | Plasma | Acoustics | Astrophysics | Propagation | Magnetic fields

Solitary wave | Extraterrestrial Physics, Space Sciences | Dusty plasma | Astrophysics and Astroparticles | Astrobiology | Periodic wave | Kink and anti-kink waves | Cosmology | Physics | Astronomy, Observations and Techniques | ASTRONOMY & ASTROPHYSICS | NONEXTENSIVE STATISTICS | CRYSTALS | SOLAR-SYSTEM | SOLITON | Geomagnetism | Plasma physics | Wave propagation | Magnetosphere | Electrons | Plasma | Acoustics | Astrophysics | Propagation | Magnetic fields

Journal Article

理论物理通讯：英文版, ISSN 0253-6102, 2008, Volume 50, Issue 8, pp. 411 - 416

In the present paper, under investigation is a nonisospectral modified Kadomtsev-Petviashvili equation, which is shown to have two Painleve branches through...

符号计算 | 变换形式 | 物理 | 求解方法 | Grammian solution | Nonisospectral modified Kadomtsev-Petviashvili equation | Symbolic computation | Darboux transformation | SOLITON-LIKE SOLUTIONS | INHOMOGENEOUS OPTICAL-FIBERS | PHYSICS, MULTIDISCIPLINARY | PLASMA PHYSICS | ION-ACOUSTIC-WAVES | symbolic computation | NONLINEAR SCHRODINGER MODEL | BACKLUND TRANSFORMATION | PAINLEVE ANALYSIS | 2+1 DIMENSIONS | ARTERIAL MECHANICS | PARTIAL-DIFFERENTIAL EQUATIONS | nonisospectral modified Kadomtsev-Petviashvili equation

符号计算 | 变换形式 | 物理 | 求解方法 | Grammian solution | Nonisospectral modified Kadomtsev-Petviashvili equation | Symbolic computation | Darboux transformation | SOLITON-LIKE SOLUTIONS | INHOMOGENEOUS OPTICAL-FIBERS | PHYSICS, MULTIDISCIPLINARY | PLASMA PHYSICS | ION-ACOUSTIC-WAVES | symbolic computation | NONLINEAR SCHRODINGER MODEL | BACKLUND TRANSFORMATION | PAINLEVE ANALYSIS | 2+1 DIMENSIONS | ARTERIAL MECHANICS | PARTIAL-DIFFERENTIAL EQUATIONS | nonisospectral modified Kadomtsev-Petviashvili equation

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 05/2011, Volume 83, Issue 5, p. 056601

Under investigation is a generalized variable-coefficient forced Korteweg-de Vries equation in fluids and other fields. From the bilinear form of such...

WAVES | PHYSICS, FLUIDS & PLASMAS | SYMBOLIC COMPUTATION | DYNAMICS | ELASTIC TUBE | KDV EQUATION | BACKLUND | MODEL | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI EQUATION | INTEGRABLE PROPERTIES | TRANSFORMATIONS

WAVES | PHYSICS, FLUIDS & PLASMAS | SYMBOLIC COMPUTATION | DYNAMICS | ELASTIC TUBE | KDV EQUATION | BACKLUND | MODEL | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI EQUATION | INTEGRABLE PROPERTIES | TRANSFORMATIONS

Journal Article

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