Hybrid solutions for the (2+1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid mechanics

2021 ◽  
Vol 152 ◽  
pp. 111355
Author(s):  
Fei-Yan Liu ◽  
Yi-Tian Gao ◽  
Xin Yu ◽  
Lei Hu ◽  
Xi-Hu Wu
Keyword(s):  
Fluid Mechanics ◽  
Variable Coefficient ◽  
Hybrid Solutions ◽  
Dimensional Variable

scholarly journals Soliton Molecules and Some Novel Types of Hybrid Solutions to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Shuxin Yang ◽  
Zhao Zhang ◽  
Biao Li
Keyword(s):  
Variable Coefficient ◽  
Resonance Condition ◽  
Soliton Solutions ◽  
Wave Number ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit ◽  
Dimensional Variable

Soliton molecules of the (2 + 1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived by N-soliton solutions and a new velocity resonance condition. Moreover, soliton molecules can become asymmetric solitons when the distance between two solitons of the molecule is small enough. Finally, we obtained some novel types of hybrid solutions which are components of soliton molecules, lump waves, and breather waves by applying velocity resonance, module resonance of wave number, and long wave limit method. Some figures are presented to demonstrate clearly dynamics features of these solutions.

Soliton Solutions, Bäcklund Transformation and Wronskian Solutions for the (2+1)-Dimensional Variable-Coefficient Konopelchenko–Dubrovsky Equations in Fluid Mechanics

2012 ◽  
Vol 67 (3-4) ◽  
pp. 132-140
Author(s):  
Peng-Bo Xu ◽  
Yi-Tian Gao
Keyword(s):  
Shear Flow ◽  
Fluid Mechanics ◽  
Shallow Water ◽  
Bilinear Form ◽  
Water Waves ◽  
Variable Coefficient ◽  
Soliton Solutions ◽  
Shallow Water Waves ◽  
Stratified Shear Flow ◽  
Dimensional Variable

This paper is to investigate the (2+1)-dimensional variable-coefficient Konopelchenko- Dubrovsky equations, which can be applied to the phenomena in stratified shear flow, internal and shallow-water waves, plasmas, and other fields. The bilinear-form equations are transformed from the original equations, and soliton solutions are derived via symbolic computation. Soliton solutions and collisions are illustrated. The bilinear-form B¨acklund transformation and another soliton solution are obtained. Wronskian solutions are constructed via the B¨acklund transformation and solution

Solitons interaction and integrability for a (2+1)-dimensional variable-coefficient Broer–Kaup system in water waves

2018 ◽  
Vol 32 (08) ◽  
pp. 1750268 ◽  
Author(s):  
Xue-Hui Zhao ◽  
Bo Tian ◽  
Yong-Jiang Guo ◽  
Hui-Min Li
Keyword(s):  
Water Waves ◽  
Variable Coefficient ◽  
Soliton Solutions ◽  
Resonance Phenomenon ◽  
Bell Polynomials ◽  
Bilinear Forms ◽  
Linear Superposition ◽  
Elastic Interactions ◽  
The One ◽  
Dimensional Variable

Under investigation in this paper is a (2+1)-dimensional variable-coefficient Broer–Kaup system in water waves. Via the symbolic computation, Bell polynomials and Hirota method, the Bäcklund transformation, Lax pair, bilinear forms, one- and two-soliton solutions are derived. Propagation and interaction for the solitons are illustrated: Amplitudes and shapes of the one soliton keep invariant during the propagation, which implies that the transport of the energy is stable for the (2+1)-dimensional water waves; and inelastic interactions between the two solitons are discussed. Elastic interactions between the two parabolic-, cubic- and periodic-type solitons are displayed, where the solitonic amplitudes and shapes remain unchanged except for certain phase shifts. However, inelastically, amplitudes of the two solitons have a linear superposition after each interaction which is called as a soliton resonance phenomenon.

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