scholarly journals Time-Dependent Polynomials with One Double Root, and Related New Solvable Systems of Nonlinear Evolution Equations

2018 ◽  
Vol 18 (1) ◽  
pp. 153-181 ◽  
Author(s):  
Oksana Bihun ◽  
Francesco Calogero
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Time Dependent ◽  
Double Root

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.

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