Lie symmetry analysis and different types of solutions to a generalized bidirectional sixth-order Sawada–Kotera equation

Abstract

Under investigation in this work is a generalized bidirectional sixth-order Sawada–Kotera equation, which is very important in both nonlinear theory and physical application. The Lie symmetry analysis method is implemented to study the vector fields and optimal systems of the equation. Then its symmetry reductions and group invariant solutions are given by using the resulting optimal system, respectively. Furthermore, the explicit power series solutions of the equation are derived with their convergence analysis. Finally, by using the Bell’s polynomials, a straightforward way is presented to construct its bilinear form, solitary wave solution and periodic wave solution with detailed derivation.