Exploring nonlinear dispersive waves in a disordered medium: an analysis using ϕ⁶ model expansion method

This study investigates a stochastic nonlinear Schrödinger equation (1+1) dimensional with a random potential. The equation under consideration is crucial in the study of the evolution of nonlinear dispersive waves in a completely disordered medium. By employing the ϕ⁶ model expansion technique, we will derive stochastic exact solutions for this stochastic partial differential equation. The obtained solutions can be expressed as exponential type and the results show that this method is effective and simple for solving such equations. Additionally, the study of nonlinear equations in a random environment is important as solitons are known to be stable against mutual collisions and behave like particles. However, it is difficult to describe realistic physical phenomena with variable or constant coefficient nonlinear equations.