Complete integrability, gauge equivalence and Lax representation of inhomogeneous nonlinear evolution equations

1992 ◽  
Vol 92 (3) ◽  
pp. 952-963 ◽  
Author(s):  
V. S. Gerdjikov
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Complete Integrability ◽  
Nonlinear Evolution Equations ◽  
Lax Representation ◽  
Gauge Equivalence

Kink solutions of two generalized fifth-order nonlinear evolution equations

2021 ◽  
Author(s):  
Li-Li Zhang ◽  
Jian-Ping Yu ◽  
Wen-Xiu Ma ◽  
Chaudry Masood Khalique ◽  
Yong-Li Sun
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Dispersion Relations ◽  
Complete Integrability ◽  
Nonlinear Evolution Equations ◽  
The Other ◽  
Fifth Order

In this paper, two generalized fifth-order nonlinear evolution equations are introduced and investigated: One is (1+1)-dimensional, the other is (2+1)-dimensional. The Hereman–Nuseir method is used to derive the multiple kink solutions and singular kink solutions, and the conditions for the cases of complete integrability of these two equations. Meanwhile, it is found that these equations have completely different dispersion relations and physical structures. The corresponding graphs with specific parameters are given to show the effectiveness and validness of the obtained results.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

scholarly journals The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations

2021 ◽  
Vol 22 ◽  
pp. 103979
Author(s):  
Nauman Raza ◽  
Muhammad Hamza Rafiq ◽  
Melike Kaplan ◽  
Sunil Kumar ◽  
Yu-Ming Chu
Keyword(s):  
Local Time ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
The Unified Method ◽  
Unified Method

scholarly journals Motion of curves and surfaces and nonlinear evolution equations in (2+1) dimensions

1998 ◽  
Vol 39 (7) ◽  
pp. 3765-3771 ◽  
Author(s):  
M. Lakshmanan ◽  
R. Myrzakulov ◽  
S. Vijayalakshmi ◽  
A. K. Danlybaeva
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Curves And Surfaces
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