Analysis of (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation via Lax pair investigation and group transformation method

Singular manifolds method (SMM) is utilized to detect the Lax pair and Bäcklund transformation of (3+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation. An extension of group transformation method with three parameters is exploited in transforming the Lax pair directly to a system of ordinary differential equations (ODEs). Two cases of similarity variables are considered resulting in solvable systems of ODEs. New analytical solutions are attained and graphed containing some soliton waves. Some of these solutions are applicable of plasma explosions and fluid dynamics. Both of investigation of Lax pair of (3+1)-dimensional evolution equations and three parameters group method are seldom utilized in this kind of evolution equations.