RETRACTED: Lie symmetry analysis, optimal system and exact solutions for variable-coefficients (2 + 1)-dimensional dissipative long-wave system

Abstract

In this article, the symmetry, optimal system, exact solutions and conservation laws of (2+1)-dimensional dissipative long-wave system with variable-coefficients (vcDLW) are investigated. These are important for mathematicians and physicists to solve problems about shallow water waves. The infinitesimal generators of independent variables are solved using Lie symmetry analysis method firstly. Based on the linear combination of vector fields, the representative elements of one-dimensional subalgebras optimal system are introduced by Olver's method. Some new exact solutions of the (2+1)-dimensional vcDLW are obtained by using Riccati equation method and tanh expansion method, such as kink solutions and soliton solutions. It is shown that this system has different solutions for different reductions. These solutions are important for describing a number of physical phenomena. The difference in this article is that the coefficients of some terms are functions. The unique feature of this article is that we can obtain many different types of equations when the coefficient functions change. This makes the (2+1)-dimensional vcDLW describe more general physical phenomena. In addition, the dynamical behaviour of the exact solutions of the (2+1)-dimensional vcDLW is analysed. And the evolution of several types of solutions is studied depending on the change in time. This process can be described better with the help of figures. Finally, The conservation laws of the (2+1)-dimensional vcDLW are obtained using the new conservation theorem with two modificatory rules.