Lie symmetries and invariant solutions for three generalized short pulse equations

The basic idea of Lie symmetry analysis, LSA, is to find the similarity solutions, invariant solutions and the reduction of order of non-linear PDEs that are formed under a local one-parameter Lie group of transformations of dependent and independent variables. Sophus Lie was a Norwegian mathematician whose work played fundamental role for attaining the solutions of non-linear PDEs and their systems by following a certain algorithm which is comparatively more easy than other complex methods. In this article, LSA is applied for further three different new cases of non-linear short pulse equation (SPE). We in fact obtain invariant solutions and reductions under the one-parameter \('\epsilon '\) Lie group of transformations. Then we derive traveling wave solutions for the first case of SPE by sine-cosine method.