New Exact Traveling Wave Solutions to the Kawahara Equation using the tanh (?) Expansion Method

Abstract

Existing approaches to solving the Kawahara equation rely on nonlinear terms with positive powers in auxiliary ordinary differential equations, limiting the number of possible solutions. This paper proposes a tanh (?) expansion method that uses a novel form that accounts for nonlinear terms with both positive and negative powers of tanh (?) to discover six families of exact traveling wave solutions; four of these families are novel, while the other two correspond to solutions previously discovered in the literature. Some solutions with various coefficient values corresponding to the six discovered family solutions are plotted to show how they behave. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.