The exponential behavior of a stochastic Cahn-Hilliard-Navier-Stokes model with multiplicative noise

Abstract

This paper is concerned with the Camassa-Holm-KP equation, which is a model for shallow water waves. By using the analysis of the phase space, we obtain some qualitative properties of equilibrium points and existence results of solitary wave solutions for the Camassa-Holm-KP equation without delay. Furthermore we show the existence of solitary wave solutions for the equation with a special local delay convolution kernel by combining the geometric singular perturbation theory and invariant manifold theory. In addition, we discuss the existence of solitary wave solutions for the Camassa-Holm-KP equation with strength $ 1 $ of nonlinearity, and prove the monotonicity of the wave speed by analyzing the ratio of the Abelian integral.