scholarly journals Integrable nonlinear evolution equations with time‐dependent coefficients

1993 ◽  
Vol 34 (11) ◽  
pp. 5140-5158 ◽  
Author(s):  
Benno Fuchssteiner
2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Li-hua Zhang

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.


2021 ◽  
Author(s):  
Yuxin Qin ◽  
Yinping Liu ◽  
Guiqiong Xu

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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