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Optimal system and approximate solutions of nonlinear dissipative media
Author(s) -
Ruggieri Marianna,
Speciale Maria Paola
Publication year - 2019
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.5835
Subject(s) - mathematics , homogeneous space , nonlinear system , dissipative system , impossibility , invariant (physics) , dissipation , algebraic number , mathematical analysis , mathematical physics , geometry , physics , quantum mechanics , thermodynamics , political science , law
In this paper, the problem of approximate symmetries of a class of nonlinear wave equations with a small nonlinear dissipation has been investigated. In order to compute the first‐order approximate symmetry, we have applied the method that was proposed by Valenti basically based on the expansion of the dependent variables in perturbation series but removing the drawback of the impossibility to work in hierarchy in calculating symmetries. The algebraic structure of the approximate symmetries is discussed, an optimal system of one‐dimensional subalgebras is defined and constructed, and, finally, some invariant solutions corresponding to the resulted symmetries are obtained.