Invariance analysis, exact solutions and conservation laws of (2+1)-dimensional dispersive long wave equations

In this article, some new exact explicit solutions of (2+1)-dimensional dispersive long wave (DLW) equations are obtained by using the similarity transformation method under some restrictions imposed on the infinitesimals. This method reduces the dimension of PDEs by one after applying once. By choosing the suitable values of arbitrary functions involved in the expressions of infinitesimals, the system of PDEs is converted into the system of ODEs with the help of similarity variables. Under the suitable choice of arbitrary constants, the graphical representation of the obtained solutions are shown in order to highlight the importance of the study. The adjoint table, conservation laws and optimal system of DLW system are also obtained.