Physical properties for bidirectional wave solutions to a generalized fifth-order equation with third-order time-dispersion term

Abstract

Higher-order temporal-dispersion partial differential equations have its capability to visualize the evolution of steeper-waves for shorter wave-length better than the higher-order KdV does. In this work, we study the physical-structure propagations of generalized fifth-order nonlinear equation involving time-dispersion term. This model is recently proposed by Wazwaz (Xu and Wazwaz, 2020) and is considered to be the first type of integrable equations that involves a third-order time-dispersion term. We implement three functional-methods to seek solitary wave solutions to the proposed model. 2D-plots are provided to recognize the type of the obtained solutions. Finally, we propose some physical properties of the bidirectional waves that such model admits.

Keywords

• Fifth-order nonlinear equation
• Third-order time-dispersion term
• Tanh–coth function method
• Modified kudryashov expansion method
• Rational sine–cosine method