AUTHOR=Yang Ben , Song Yunjia , Wang Zenggui 

TITLE=Lie symmetry analysis and exact solutions of the (3+1)-dimensional generalized Shallow Water-like equation

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1131007

DOI=10.3389/fphy.2023.1131007

ISSN=2296-424X

ABSTRACT=<p>In this article, (3+1)-dimensional generalized Shallow Water-like (gSWl) equation is discussed. The infinitesimal generators of the equation are derived by using the Lie symmetry analysis method. The optimal system is obtained based on the adjoint table of the generators of the equation. Exact solutions of the equation are constructed by applying symmetry reduction, Exp<inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfenced open="(" close=")"><mml:mrow><mml:mo>−</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>ξ</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mfenced></mml:math></inline-formula> expansion method, Exp-function expansion method, Riccati equation method, and <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfenced open="(" close=")"><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:mi>G</mml:mi></mml:mrow></mml:mfenced></mml:math></inline-formula> expansion method. For analyzing the dynamical behavior of the solutions, we derive the physical structures of dark soliton, kink wave, and periodic solutions <italic>via</italic> numerical simulations.</p>