Vishakha Jadaun . Navnit Jha

Vishakha Jadaun, Department of Mathematics, Malla Reddy University, Hyderabad, India E-mail: vishakhasjadaun@gmail.com , Navnit Jha, Department of Mathematics, South Asian University, New Delhi, India E-mail: navnitjha@sau.ac.in

Received in final form on December 18, 2022

Abstract
The Lie group of infinitesimal transformations technique and similarity reduction is performed for obtaining an exact invariant solution to generalized Kadomstev-Petviashvili-Boussinesq (gKPB) equation in (3+1)-dimensions. We obtain generators of infinitesimal transformations, which provide us with a set of Lie algebras. In addition, we get geometric vector fields, a commutator table of Lie algebra, and a group of symmetries. A detailed geometrical framework related to the nature of the solutions possessing traveling wave, bright and dark soliton, standing wave with multiple breathers, and one-dimensional kink, for the appropriate values of the parameters involved. It is observed that there is a qualitative difference between dark soliton and bright soliton. Multiple breathers are detected, a breather is a nonlinear wave wherein energy concentrates in a local and oscillatory manner. A partially standing and partially traveling wave with changing amplitude is also observed and it is seen that breathers are localized solutions with varying amplitude.

Keywords
(3+1) - dimensional Generalised Kadomtsev-Petviashvili-Boussinesq equation, Lie symmetries, Similarity transformations method, Infinitesimal generator, Soliton solutions

Cite This Article
Vishakha Jadaun and Navnit Jha,Lie Symmetry Analysis for Soliton Solutions of Generalised Kadomtsev-Petviashvili-Boussinesq Equation in (3 + 1)-dimensions, J. Innovation Sciences and Sustainable Technologies, 3(1)(2023), 23 - 40. https://doie.org/10.0421/JISST.2023834560

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