THE BREATHER WAVE SOLUTIONS, M-LUMP SOLUTIONS AND SEMI-RATIONAL SOLUTIONS TO A (2+1)-DIMENSIONAL GENERALIZED KORTEWEG-DE VRIES EQUATION | Zendy

Hui Wang | Zendy; ShouFu Tian | Zendy; TianTian Zhang | Zendy; Yi Chen | Zendy

Open Access

THE BREATHER WAVE SOLUTIONS, M-LUMP SOLUTIONS AND SEMI-RATIONAL SOLUTIONS TO A (2+1)-DIMENSIONAL GENERALIZED KORTEWEG-DE VRIES EQUATION

Author(s) -

Hui Wang,

ShouFu Tian,

TianTian Zhang,

Yi Chen

Publication year - 2020

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/20190011

Subject(s) - breather , bilinear form , korteweg–de vries equation , soliton , bilinear interpolation , traveling wave , mathematics , one dimensional space , mathematical physics , formalism (music) , mathematical analysis , nonlinear system , polynomial , limit (mathematics) , rogue wave , physics , quantum mechanics , art , musical , visual arts , statistics

Under investigation in this work is a (2+1)-dimensional generalized Korteweg-de Vries equation, which can be used to describe many nonlinear phenomena in plasma physics. By using the properties of Bell’s polynomial, we obtain the bilinear formalism of this equation. The expression of N -soliton solution is established in terms of the Hirota’s bilinear method. Based on the resulting N -soliton solutions, we succinctly show its breather wave solutions. Furthermore, with the aid of the corresponding soliton solutions, the M -lump solutions are well presented by taking a long wave limit. Two types of hybrid solutions are also represented in detail. Finally, some graphic analysis are provided in order to better understand the propagation characteristics of the obtained solutions.

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