scholarly journals An investigation to the nonlinear (2 + 1)-dimensional soliton equation for discovering explicit and periodic wave solutions

2021 ◽  
pp. 104013
Author(s):  
M. Akher Chowdhury ◽  
M. Mamun Miah ◽  
H.M. Shahadat Ali ◽  
Yu-Ming Chu ◽  
M.S. Osman
Keyword(s):  
Periodic Wave ◽  
Soliton Equation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Dimensional Soliton

scholarly journals New periodic wave solutions of (3+1)-dimensional soliton equation

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 169-176 ◽  
Author(s):  
Jiangen Liu ◽  
Pinxia Wu ◽  
Yufeng Zhang ◽  
Lubin Feng
Keyword(s):  
Evolution Equations ◽  
Periodic Wave ◽  
Soliton Equation ◽  
Periodic Wave Solutions ◽  
Linear Evolution ◽  
Wave Solutions ◽  
Hirota Bilinear Form ◽  
Powerful Approach ◽  
Dimensional Soliton ◽  
Linear Evolution Equations

In this paper, associating with the Hirota bilinear form, the three-wave method, which is applied to construct some periodic wave solutions of (3+1)-dimensional soliton equation, is a powerful approach to obtain periodic solutions for many non-linear evolution equations in the integrable systems theory.

Periodic-wave solutions and asymptotic properties for a (3+1)-dimensional generalized breaking soliton equation in fluids and plasmas

2021 ◽  
pp. 2150344
Author(s):  
Rui-Dong Chen ◽  
Yi-Tian Gao ◽  
Xin Yu ◽  
Ting-Ting Jia ◽  
Gao-Fu Deng ◽  
...  
Keyword(s):  
Asymptotic Properties ◽  
Theta Functions ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Soliton Equation ◽  
One Dimensional ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Riemann Theta Functions ◽  
The One

In this paper, a (3+1)-dimensional generalized breaking soliton equation is investigated. Based on the one- and two-dimensional Riemann theta functions, one- and two-periodic-wave solutions are derived. We observe that the one-periodic wave is one-dimensional and is viewed as a superposition of the overlapping waves, placed one period apart. With certain parameters, the symmetric feature appears in the two-periodic wave, and the two-periodic wave degenerates to the one-periodic wave. With the series expansions, we explore the relations between the soliton and periodic-wave solutions. According to those relations, asymptotic properties for the periodic-wave solutions to approach to the soliton solutions under certain amplitude conditions are derived.

Folded Localized Excitations and Chaotic Patterns in a (2+1)-Dimensional Soliton System

2008 ◽  
Vol 63 (3-4) ◽  
pp. 121-126 ◽  
Author(s):  
Song-Hua Ma ◽  
Jian-Ping Fang ◽  
Chun-Long Zheng
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Localized Excitations ◽  
Dimensional Soliton ◽  
Variable Separation Approach

Starting from an improved mapping approach and a linear variable separation approach, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for the (2+1)-dimensional breaking soliton system are derived. Based on the derived solitary wave solution, we obtain some special folded localized excitations and chaotic patterns.

Applications of F -expansion to Periodic Wave Solutions for Variant Boussinesq Equations

2005 ◽  
Vol 44 (3) ◽  
pp. 396-400 ◽  
Author(s):  
Yue-Ming Wang ◽  
Xiang-Zheng Li ◽  
Sen Yang ◽  
Ming-Liang Wang
Keyword(s):  
Boussinesq Equations ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variant Boussinesq Equations
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