Complete group classification and exact solutions to the extended short pulse equation

In this paper, the complete group classification is performed on the extended short pulse equation (ESPE), which including many important non-linear wave equations as its special cases. In the sense of geometric symmetry, all of the vector fields of the equation are obtained in terms of the arbitrary parameters of the equation. Furthermore, the symmetry reductions and exact solutions to the short pulse types of equations are investigated, and the physical significance of the solutions are considered from the transformation group point of view.

► The complete group classification is performed on the ESPE in the sense of geometric symmetry.
► The exact solutions to the short pulse types of equations are obtained.
► The physical significance of the equations and solutions are considered.