Extracting wave solutions of coupled system of dual-mode variant boussinesq equation via two analytical methods

The coupled system of the dual-mode variant Boussinesq equation, an important mathematical model for explaining nonlinear two-way wave propagation and the interaction of dual wave modes in dispersive media, is the primary goal of this work. Finding precise analytical solutions of this model is crucial for comprehending intricate nonlinear wave phenomena because of its important applications in fluid dynamics, elasticity, plasma physics, and other areas of applied physics. In order to achieve this, the extended hyperbolic function method and the [Formula: see text]-expansion method are used to construct solitary wave solutions. Both methods work well for creating novel, physically significant wave shapes. Bright, dark, singular-periodic, and periodic solitary waves are among the solutions that were found. Graphical representations in two and three dimensions are used to show the dynamical properties of the obtained solutions. Additionally, modulation instability is examined using linear stability analysis, and the impact of wave speed on dual-wave interactions is examined. The obtained results show how well the suggested analytical methods work and offer important new information about nonlinear wave propagation in dispersive medium.