A study on analytical solutions and conservation laws of the cgKP occurring in straits

Abstract

The (2+1)-KP equation in its canonical generalized form i.e. cgKP relates to water waves that propagate exclusively in straits or rivers, as opposed to unbounded surfaces such as oceans. The cgKP, an example of a complex nonlinear system, is solved analytically in this article. To solve analytically the cgKP, the Lie symmetries are generated to get several novel invariant solutions to the cgKP, which are rare as far as the authors are aware. The cgKP reduces to an equivalent PDE with fewer independent variables than the original PDE. Animation profiles are utilized to better understand the obtained solutions, and they reflect transition from doubly solitons to single soliton; transition from negatons to positons and negatons; single solitons and multi solitons; annihilation of multi solitons; elastic parabolic profiles; single front parabolic and positons; multi-negatons on flat surface, and fusion of multi solitons wave types. Because of the presence of arbitrary functions in infinitesimal transformations, the Lie symmetry method has the potential to provide more variety in solutions. When compared to previously published findings, this study convincingly highlights the originality of the solutions. In the future, without assuming any relation among the arbitrary functions involved in infinitesimals, someone can explore the possibility of some more solutions. The physical character of the analytical results could help coastal engineers develop models of coastlines and ports in the current study.