Soliton solutions for the nonlocal reverse space Kundu-Eckhaus equation via symbolic calculation

The Kundu-Eckhaus (KE) equation describes the propagation of ultrashort femtosecond pulses in optical fibers. In this paper, the Hirota bilinear method is used to deal with nonlocal KE equation which is also called nonlocal integrable nonlinear Schrodinger equation with cubic and quintic nonlinearities. The N-soliton solution for the nonlocal KE equation is derived by virtue of symbolic calculation. Based on that, the exact solution expressions of two-soliton and three-soliton can be obtained. Several propagation situations are demonstrated and discussed for the combinatorial solutions of nonlocal KE equation under different parameters, including one periodic solitary wave evolution, two parallel, perpendicular and periodic solitary waves collision.

Automated summary

This paper investigates the propagation of ultrashort femtosecond pulses in optical fibers using the Kundu-Eckhaus (KE) equation. The nonlocal KE equation, also known as the nonlocal integrable nonlinear Schrodinger equation with cubic and quintic nonlinearities, is solved using the Hirota bilinear method. The N-soliton solution is derived using symbolic calculation, and the exact solution expressions for two-soliton and three-soliton are obtained. Various propagation situations, such as periodic solitary wave evolution and collision of two parallel, perpendicular, and periodic solitary waves, are demonstrated and discussed under different parameters.