Some More Invariant Solutions of (2 + 1)-Water Waves

Abstract

In view of applicability of water waves, the objective of this article is to provide some more analytical solutions of (2 + 1)-dimensional water waves i.e. Boiti–Leon–Pempinelli (BLP) system. A water wave advancing in an infinite narrow channel is described by the BLP system which generally consists of a system of nonlinear partial differential equations, therefore, to get an exact solution would be a difficult task. To solve the purpose, we have converted this system into a system of ordinary differential equations (ODEs) using similarity transformations method via Lie-group theory. The resultant system of ODEs is solved after making appropriate assumptions and choice of arbitrary functions and constants appeared therein. The established results are an extension of our previous findings (Kumar et al. in Comput Math Appl 70(3):212–221, 2015). Hence, the obtained exact solutions compromised elastic single soliton, doubly soliton, multisolitons and flipping of single solitons with passage of time.