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The four‐dimensional Martínez Alonso–Shabat equation: nonlinear self‐adjointness and conservation laws
Author(s) -
Zhang∗† ZhiYong,
Guo LeiLei,
Huang JiZheng
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3968
Subject(s) - conservation law , mathematics , homogeneous space , symmetry (geometry) , partial differential equation , nonlinear system , differential equation , construct (python library) , substitution (logic) , mathematical analysis , law , mathematical physics , geometry , computer science , political science , physics , quantum mechanics , programming language
We show that the four‐dimensional Martínez Alonso–Shabat equation is nonlinearly self‐adjoint with differential substitution and the required differential substitution is just the admitted adjoint symmetry and vice versa. By means of computer algebra system, we obtain a number of local and nonlocal symmetries admitted by the equations under study. Then such symmetries are used to construct conservation laws of the equation under study and its reductions. Copyright © 2016 John Wiley & Sons, Ltd.