On the Optimal System and Series Solutions of Fifth-Order Fujimoto-Watanabe Equations

Abstract

This paper investigates the two fifth-order Fujimoto-Watanabe equations from the perspective of the group theoretic approach. We identify the reduced equations that lead to the solutions of these high order equations. Furthermore, the corresponding solutions are found by power series due to their nonlinear characteristics. As a result, the findings of the study demonstrate the convergence of solutions for such models and identifies the travelling wave solutions.