Research Information System
INTERNATIONAL CONGRESS ON NEW TRENDS IN MECHANICS (ICNTM25) , Baku, Azerbaijan, 2 - 05 September 2025, pp.772-777, (Full Text)
Nonlinear partial differential equations (PDEs) are fundamental in modeling diverse phenomena in fluid dynamics, plasma physics, biology, and nonlinear optics. A prominent example is the Boussinesq equation, known for describing bidirectional shallow water waves with weak nonlinearity and dispersion. Its generalizations, incorporating higher-order nonlinearities and dispersion, demand advanced analytical tools to uncover exact solutions. In this work, we investigate a generalized Boussinesq-type equation using the φ6-model expansion method as an effective analytical technique capable of addressing complex nonlinear structures. This method allows us to construct novel traveling wave solutions that may capture phenomena such as dark, bright and singular solitons. The parameters of the traveling wave solutions obtained are used to display the non-linear dispersion behavior for various values, which physically represents the dynamical behavior of the waves. Fascinating graphs are used to illustrate and clarify the dynamical features of the findings.