scholarly journals Integrable nonlinear evolution equations with time‐dependent coefficients

1993 ◽  
Vol 34 (11) ◽  
pp. 5140-5158 ◽  
Author(s):  
Benno Fuchssteiner
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Time Dependent

scholarly journals Conservation Laws of Two(2+1)-Dimensional Nonlinear Evolution Equations with Higher-Order Mixed Derivatives

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Li-hua Zhang
Keyword(s):  
Conservation Laws ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Higher Order ◽  
Nonlinear Evolution Equations ◽  
Time Dependent ◽  
Mixed Derivatives ◽  
Paper Conservation ◽  
Conservation Theorem ◽  
Bbm Equation

In this paper, conservation laws for the(2+1)-dimensional ANNV equation and KP-BBM equation with higher-order mixed derivatives are studied. Due to the existence of higher-order mixed derivatives, Ibragimov’s “new conservation theorem” cannot be applied to the two equations directly. We propose two modification rules which ensure that the theorem can be applied to nonlinear evolution equations with any mixed derivatives. Formulas of conservation laws for the ANNV equation and KP-BBM equation are given. Using these formulas, many nontrivial and time-dependent conservation laws for these equations are derived.

scholarly journals New traveling wave structures for two higher dimensional nonlinear evolution equations with time-dependent coefficients: Horseshoe-like solitons and multiwave interaction solutions

2021 ◽  
Author(s):  
Yuxin Qin ◽  
Yinping Liu ◽  
Guiqiong Xu
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Variable Coefficients ◽  
Nonlinear Evolution Equations ◽  
Time Dependent ◽  
Interaction Solutions ◽  
Multiwave Interaction ◽  
Higher Dimensional ◽  
Multiwave Solutions

Abstract In this paper, by introducing new traveling wave transformations in specific nonlinear forms, a variety of new multiwave interaction solutions for two higher dimensional nonlinear evolution equations with time-dependent coefficients are investigated. These new kinds of multiwave solutions can enrich solutions of nonlinear evolution equations with variable coefficients.

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