Traveling wave solutions for the generalized (2+1)-dimensional Kundu-Mukherjee-Naskar equation

Abstract

In this paper, we consider two types of traveling wave systems of the generalized Kundu-Mukherjee-Naskar equation. Firstly, due to the integrity, we obtain their energy functions. Then, the dynamical system method is applied to study bifurcation behaviours of the two types of traveling wave systems to obtain corresponding global phase portraits in different parameter bifurcation sets. According to them, every bounded and unbounded orbits can be identified clearly and investigated carefully which correspond to various traveling wave solutions of the generalized Kundu-Mukherjee-Naskar equation exactly. Finally, by integrating along these orbits and calculating some complicated elliptic integral, we obtain all type I and type II traveling wave solutions of the generalized Kundu-Mukherjee-Naskar equation without loss.

Bending of optical solitonic beams modeled by coupled KMN equation

“…Thereafter, an extensive amount of research has been done on the KMN equation exploring its various exciting properties. Many kinds of solutions of the KMN equation were derived like higher-order rational solutions [16], optical dromions and domain walls [17,18], various optical soliton solutions having different features [19][20][21][22][23][24][25][26][27][28][29], and different analytic solutions [30][31][32][33][34][35][36][37], power series solutions [38], complex wave solutions [39,40], periodic solutions (via variational principle) [41], solitons in birefringent fiber system [42,43], etc. Integrable properties such as Lax pair, conservation laws, higher order soliton solutions via Hirota method, symmetry analysis, nonlinear self-adjointness property, etc of KMN equation have been explored in [10,13,25,40,44].…”