Dynamics of the traveling waves in a (2 + 1)-dimensional nonlinear dispersive long wave equation with three types of perturbations

We in this paper investigate the dynamics of traveling wave solutions for the (2 + 1)-dimensional nonlinear dispersive long wave (NDLW) equation under three different perturbations simultaneously: distributed delay, weak dissipation and diffusion. The traveling wave system obtained through the traveling wave transformation is a singular perturbation system, which is regularized into a near-Hamiltonian system based on geometric singular perturbation theory. By introducing the Poincaré mapping to construct the Melnikov functions and analyzing their zero distribution, the existence conditions of limit cycles for the near-Hamiltonian system are provided. Moreover, the results of numerical simulations are completely consistent with the dynamics of periodic wave, kink wave and anti-kink wave obtained from theoretical analysis.