Rational solutions and rogue waves of the generalized (2+1)-dimensional Kadomtsev–Petviashvili equation

Xie, Yingying; Yan, Yongsheng; Li, Lingfei

doi:10.1016/j.cjph.2021.11.010

Cited by 4 publications

(2 citation statements)

References 28 publications

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“…For instance, simpler firstto fourth-order rogue waves, as well as fifth-order rogue waves that were previously unpublished, are yielded by the simplified method for a generalized (2+1)dimensional Kadomtsev-Petviashvili equation. To be honest, the obtained results in this paper substantially improve or complement the corresponding conditions in the references [17,18]. As a consequence, this paper gives a new idea to derive high-order rogue waves for the generalized (2+1)-dimensional Kadomtsev-Petviashvili equation.…”

supporting

confidence: 66%

A simplified symbolic computation method based on Hirota bilinear equations for constructing multiple-order rogue waves

Tang,

Zeng

2024

Preprint

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The computation of higher-order rogue waves can be a time-consuming process.Hirota bilinear equations with controllable centers for all orders of rogue wave solutions can be solved by a simplified symbolic computation method.Only one-third of the computational effort needed by the original method is required by the simplified one, for very high orders. For instance, simpler first- to fourth-order rogue waves, as well as fifth-order rogue waves that were previously unpublished, are yielded by the simplified method for a generalized (2+1)-dimensional Kadomtsev-Petviashvili equation. To be honest, the obtained results in this paper substantially improve or complement the corresponding conditions in the references [17,18]. As a consequence,~this paper gives a new idea to derive high-order rogue waves for the generalized (2+1)-dimensional Kadomtsev-Petviashvili equation.

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supporting

confidence: 66%

A simplified symbolic computation method based on Hirota bilinear equations for constructing multiple-order rogue waves

Tang,

Zeng

2024

Preprint

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“…simulates the weak dispersion and transverse long wave motion of a one dimensional stable soliton solution in a weakly dispersive medium [31][32][33]. We are interested in and study its more complicated (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like (KPB-like) equation…”

Section: Introductionmentioning

confidence: 99%

Rational and semi-rational solution to the (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation

Chen

Deng

2023

Phys. Scr.

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In the paper, we take the (3+1)-dimensional KP-Boussinesq-like equation as an instance and utilize long wave limit approach to generate rational solution and semi-rational solution from the N-order soliton solution. For $ N=2,3 $, with specific parametric constraints, we have constructed rational solutions which can be presented as first order line rogue wave and single breather from two-soliton solution, and semi-rational solution is classified as first order kink-shaped rogue wave and a hybrid of breather and one soliton from three-soliton solution. For $N=4$, the rational solution includes second order line rogue wave, double breather, interaction between two breathers and a hybrid of breather and line rogue wave. The semi-rational solution contains second order kink-shaped rogue wave and interaction between breather, soliton and line rogue wave. In addition, we give mathematical expressions for higher N-order rational solution.

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Computational investigation on a nonlinear dispersion model with the weak non-local nonlinearity in quantum mechanics

et al. 2022

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Rational solutions and rogue waves of the generalized (2+1)-dimensional Kadomtsev–Petviashvili equation

Cited by 4 publications

References 28 publications

A simplified symbolic computation method based on Hirota bilinear equations for constructing multiple-order rogue waves

A simplified symbolic computation method based on Hirota bilinear equations for constructing multiple-order rogue waves

Rational and semi-rational solution to the (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation

Computational investigation on a nonlinear dispersion model with the weak non-local nonlinearity in quantum mechanics

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