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Solitary wave solution and conservation laws of higher dimensional Zakharov‐Kuznetsov equation with nonlinear self‐adjointness
Author(s) -
Ali Muhammad Nasir,
Husnine Syed Muhammad,
Ak Turgut,
Atangana Abdon
Publication year - 2018
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.5180
Subject(s) - conservation law , mathematics , nonlinear system , homogeneous space , dimension (graph theory) , symmetry (geometry) , mathematical analysis , mathematical physics , pure mathematics , physics , geometry , quantum mechanics
In this paper, we consider (1 + n) ‐dimensional Zakharov‐Kuznetsov (ZK) equation for nonlinear self‐adjointness and symmetries. It is proved that the equation is nonlinearly self‐adjoint and its symmetries are computed. The conservation laws are obtained by using new general conservation theorem of Ibragimov for (1 + n) ‐dimension and particularly for (1 + 3)‐dimensional ZK equation. Multiplier method is also used to find more conservation laws for (1 + 3)‐dimensional ZK equation and symmetry reduction technique is used to calculate the solitary wave solution.