Peakon, Cuspon, Compacton, and Loop Solutions of a Three-Dimensional 3DKP(3, 2) Equation with Nonlinear Dispersion

Zhao, Haixia; Qiao, Lijing; Tang, Shengqiang

doi:10.1155/2014/934987

Cited by 3 publications

(2 citation statements)

References 24 publications

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“…See, e.g., Ref. [22,23] where such problems are overlooked for nonlinearly dispersive KP-type equations. Indeed, the K N (m, n) equation admits many formal piecewise soltuions that are only continuous at the cut off, which are not reported in the present paper because they fail to lie in any physically meaning function space.…”

Section: Discussionmentioning

confidence: 99%

Nonlinearly dispersive KP equations with new compacton solutions

Anco¹,

Gandarias²

2021

Preprint

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An exhaustive classification of compacton solutions is carried out for a generalization of the Kadomtsev-Petviashvili (KP) equation involving nonlinear dispersion in two and higher spatial dimensions. In particular, precise conditions are given on the nonlinearity powers in this equation under which a travelling wave can be cut off to obtain a compacton. It is shown that there are no compactons which are classical (strong) solutions. Instead, the compactons consist of pointwise distributional solutions as well as weak solutions of an integrated from of the ODE for travelling waves. Weak-compacton solutions constitute a new type of solution which has not been studied previously. An explicit example is obtained in which the compacton profile is a power of an expression that is linear in the travelling wave variable and its sine. Explicit compactons with profiles given by powers of a cosine, a sine, Jacobi sn and cn functions, and a quadratic function are also derived. In comparison, explicit solitary waves of the generalized KP equation are found to have profiles given by a power of a sech and a reciprocal quadratic function. Kinematic properties of all of the different types of compactons and solitary waves are discussed, along with conservation laws of the generalized KP equation.

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Section: Discussionmentioning

confidence: 99%

Nonlinearly dispersive KP equations with new compacton solutions

Anco¹,

Gandarias²

2021

Preprint

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“…To discuss the existence of peakon, pseudo‐peakon, cuspon and smooth and solitary wave solutions, we need to use the following two lemmas relating to the singular straight line .…”

Section: Exact Explicit Peakon Pseudo‐peakon Cuspon and Smooth And mentioning

confidence: 99%

Peakon, pseudo‐peakon, cuspon and smooth solitons for a nonlocal Kerr‐like media

Zhao

Tang

2016

Math Methods in App Sciences

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This paper presents all possible exact explicit peakon, pseudo‐peakon, cuspon and smooth solitary wave solutions for a nonlocal Kerr‐like media. We apply the method of dynamical systems to analyze the dynamical behavior of the traveling wave solutions and their bifurcations depending on the parameters of the system. We present peakon, pseudo‐peakon, cuspon soliton solution in an explicit form. We also have obtained smooth soliton. Mathematical analysis and numeric graphs are provided for those soliton solutions of the nonlocal Kerr‐like media. Copyright © 2016 John Wiley & Sons, Ltd.

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Nonlinearly dispersive KP equations with new compacton solutions

Anco,

Gandarias

2024

Nonlinear Analysis: Real World Applications

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Peakon, Cuspon, Compacton, and Loop Solutions of a Three-Dimensional 3DKP(3, 2) Equation with Nonlinear Dispersion

Cited by 3 publications

References 24 publications

Nonlinearly dispersive KP equations with new compacton solutions

Nonlinearly dispersive KP equations with new compacton solutions

Peakon, pseudo‐peakon, cuspon and smooth solitons for a nonlocal Kerr‐like media

Nonlinearly dispersive KP equations with new compacton solutions

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