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Purpose -The purpose of this paper is to propose a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions of two-space-dimensional quasilinear hyperbolic partial differential equations subject to appropriate Dirichlet and Neumann boundary conditions. Design/methodology/approach -The PDQM reduced the equations into a system of second order linear differential equation. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations. Findings -The accuracy of the proposed method is demonstrated by several test examples. The numerical results are found to be in good agreement with the exact solutions. The proposed technique can be applied easily for multidimensional problems. Originality/value -The main advantage of the present scheme is that the scheme gives very accurate and similar results to the exact solutions by choosing less number of grid points and the problem can be solved up to big time. The good thing of the present technique is that it is easy to apply and gives us better accuracy in less numbers of grid points as comparison to the other numerical techniques.

The current work is devoted for operating the Lie symmetry approach, to coupled complex short pulse equation. The method reduces the coupled complex short pulse equation to a system of ordinary differential equations with the help of suitable similarity transformations. Consequently, these systems of nonlinear ordinary differential equations under each subalgeras are solved for traveling wave solutions. Further, with the help of similarity variable, similarity solutions and traveling wave solutions of nonlinear ordinary differential equation, complex soliton solutions of the coupled complex short pulse equation are obtained which are in the form of sinh, cosh, sin and cos functions.

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