Finance

Physics

Korteweg–de Vries equation

Nonlinear system

Integrable system

Mathematics

Term (time)

Biology

Partial differential equation

Optics

Mathematical analysis

Order (exchange)

Economics

Dispersion (optics)

Ecology

Type (biology)

Quantum mechanics

Applied mathematics

Wave equation

Results in Physics

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.

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