Disturbance solutions for the long–short-wave interaction system using bi-random Riccati–Bernoulli sub-ODE method

Abstract

This article applied the Riccati–Bernoulli (RB) sub-ODE method in order to get new exact solutions for the long–short-wave interaction (LS) equations. Namely, we obtain deterministic and random solutions, since we consider the proposed method in deterministic and random cases. The RB sub-ODE technique gives the travelling wave solutions in forms of hyperbolic, trigonometric and rational functions. It is shown that the proposed method gives a robust mathematical tool for solving nonlinear wave equations in applied science. Furthermore, some bi-random variables and some random distributions are used in random case corresponding to the LS system. The stability for the obtained solutions in random case is considered. In addition, there is a display of several numerical simulations, which helps to understand the physical phenomena of these soliton wave solutions.

Keywords

• riccati–bernoulli sub-ode technique
• long–short-wave interaction equations
• bäcklund transformation
• travelling wave solutions
• exact solutions
• random distributions
• second-order random variables
• stability