The solitary wave, kink and anti-kink solutions coexist at the same speed in a perturbed nonlinear Schrodinger equation

Persistence of the traveling wave solutions of a perturbed higher order nonlinear Schrodinger equation with distributed delay is studied by the geometric singular perturbation theory. The solitary wave, kink and anti-kink solutions are proved to coexist simultaneously at the same speed c by combing the Melnikov method and the bifurcation analysis. Interestingly, a new type of traveling wave solution possessing crest, trough and kink (anti-kink) is discovered. Further, numerical simulations are carried out to confirm the theoretical results.

Automated summary

The persistence of traveling wave solutions of a perturbed higher order nonlinear Schrodinger equation with distributed delay is investigated using geometric singular perturbation theory. The coexistence of solitary wave, kink, and anti-kink solutions at the same speed c is proven by combining the Melnikov method and bifurcation analysis. Interestingly, a new type of traveling wave solution with crest, trough, and kink (anti-kink) is discovered. Numerical simulations are performed to validate the theoretical findings.