Solutions of 1D Hyperbolic Quasi-linear Partial Differential Equations by Variational Iteration Method

Abstract In this paper, we have constructed one dimensional (1D) hyperbolic quasi-linear partial differential equations (HQLPDE) considering three cases. In the first two cases, we have considered the Cauchy data in the form of exponential curve. The initial value problem (IVP) is mentioned as sin x in the third case. All the three cases are associated with time. We have obtained the solutions by using variational iteration method (VIM). We found that the solutions represent flat surface during the initial stage. Further we found exponential surface in the 1st two cases where as the third case yield curved surface with respect to distance and time. Mathematics subject classification: 35Lxx, 35L04