Novel wave solutions for the sixth-order Boussinesq equation arising in nonlinear lattice dynamics

Abstract

This study examines a class of Boussinesq equations with sixth-order using two promising analytical methods. The equation in question is among the frontier evolution equations with significant relevance in nonlinear lattice dynamics. To study this model, the Kudryashov method and the modified auxiliary equation method are employed due to their analytical precision in constructing several exact wave solutions for the model under examination. As expected, the methods yield many valid solution sets that satisfy all the underlying assumptions of the model. Finally, some of the obtained wave solutions are graphically illustrated, taking into account the parameter values of the model.

Keywords

• higher-order evolution equations
• boussinesq equation
• exact wave solutions
• kudryashov method
• modified auxiliary equation method