Lie group analysis with the optimal system, generalized invariant solutions, and an enormous variety of different wave profiles for the higher-dimensional modified dispersive water wave system of equations
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, 110007, New Delhi, Delhi, India
2 Department of Mathematics, Zhejiang Normal University, 321004, Jinhua, Zhejiang, China
3 Department of Mathematics, King Abdulaziz University, 21589, Jeddah, Saudi Arabia
4 Department of Mathematics and Statistics, University of South Florida, 33620-5700, Tampa, FL, USA
5 School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, 2735, Mmabatho, South Africa
6 Department of Mathematics, Daulat Ram College, University of Delhi, 110007, New Delhi, Delhi, India
Accepted: 1 May 2023
Published online: 22 May 2023
In this work, the method of the Lie group of invariance is used to explore a (2+1)-dimensional modified dispersive water wave (mDWW) system of equations. This system is used to describe dispersive, nonlinear, long gravity waves traveling in two horizontal directions on shallow water. Calculating infinitesimal generators through symbolic computation is accomplished. Employing infinitesimal generators, the vector fields are obtained, and corresponding to the vector fields, the commutator table and the adjoint table are constructed. Furthermore, based on the adjoint table, the one-dimensional optimal system of subalgebras is obtained. With the aid of the optimal system, similarity reductions are performed for different cases. Through similarity reductions, the considered system of nonlinear partial differential equations (PDEs) is converted to a system of ordinary differential equations (ODEs) using Lie symmetry analysis, resulting in closed-form group-invariant solutions. The graphs consist of the periodic solitons. Dromions and peakon excitations are revealed in the graphical representations of the solutions. Using these graphs, mathematicians and physicists can follow complicated physical phenomena more efficiently. The mDWW system is fully integrated and has numerous applications in tidal waves and ocean tsunamis.
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