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Optimal solutions of a (3 + 1)‐dimensional B‐Kadomtsev‐Petviashvii equation
Author(s) -
Saleh Rash,
Sadat Rahma,
Kassem Magda
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.6001
Subject(s) - mathematics , ode , riccati equation , infinitesimal , symmetry (geometry) , nonlinear system , kadomtsev–petviashvili equation , lie group , reduction (mathematics) , mathematical analysis , pure mathematics , burgers' equation , partial differential equation , geometry , physics , quantum mechanics
We explored and specialized new Lie infinitesimals for the (3 + 1)‐dimensional B‐Kadomtsev‐Petviashvii (BKP) using the commutation product, which results a system of nonlinear ODEs manually solved. Through two stages of Lie symmetry reduction, (3 + 1)‐dimensional BKP equation is reduced to nonsolvable nonlinear ODEs using various combinations of optimal Lie vectors. Using the integration and Riccati equation methods, we investigate new analytical solutions for these ODEs. Back substituting to the original variables generates new solutions for BKP. Some selected solutions illustrated through three‐dimensional plots.