Symmetries, optimal system, exact and soliton solutions of ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si113.svg"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo linebreak="goodbreak">+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> )-dimensional Gardner-KP equation
Amjad Hussain, Ashreen Anjum, M. Junaid-U-Rehman, Ilyas Khan, Mariam A. Sameh, Amnah S. Al‐Johani
Abstract
In this research article, the (3+1)-dimensional nonlinear Gardner–Kadomtsov–Petviashvili (Gardner-KP) equation which depicts the nonlinear modulation of periodic waves, is analyzed through the Lie group-theoretic technique. Considering the Lie invariance condition, we find the symmetry generators. The proposed model yields eight-dimensional Lie algebra. Moreover, an optimal system of sub-algebras is computed, and similarity reductions are made. The considered nonlinear partial differential equation is reduced into ordinary differential equations (ODEs) by utilizing the similarity transformation method (STM), which has the benefit of yielding a large number of accurate traveling wave solutions. These ODEs are further solved to get closed-form solutions of the Gardner-KP equation in some cases, while in other cases, we use the new auxiliary equation method to get its soliton solutions. The evolution profiles of the obtained solutions are examined graphically under the appropriate selection of arbitrary parameters.