Existence results of solitary wave solutions for a delayed Camassa-Holm-KP equation (Q2062530)

This paper considers the equation \[(u_t - u_{xxt} + 2ku_x - a(f \ast u)u^{n-1}u_x + \tau u_{xx})_x + u_{yy} = 0,\] where \[f \ast u(x, y, t) = \int^t_{-\infty}f(t-s)u(x, y, s)ds,\] and the kernel \(f : [0, +\infty) \to [0, +\infty)\) with \(\int^t_0 f(t)dt= 1.\) This is a Camassa-Holm (CH) and Kadomtsev-Petviashivilli (KP) type equation. Some qualitative properties of equilibrium points and existence results of solitary wave solutions for the equation without delay or with a special local delay convolution kernel are presented.