Chen, X., Yang, J. and Lam, W.K. (2006) N-Soliton Solution for the Derivative Nonlinear Schrödinger Equation with Nonvanishing Boundary Conditions. Journal of Physics A: Mathematical and General, 39, 3263-3274.
https://doi.org/10.1088/0305-4470/39/13/006

has been cited by the following article:

• TITLE: Mixed Soliton Solutions of MNLS/DNLS Equations Based on Hirota Method

  AUTHORS: Jiarui Hu, Guoquan Zhou

  KEYWORDS: MNLS Equation, DNLS Equation, Nonlinear Equation, Hirota’s Bilinear Derivative Transform, Soliton, Breather

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.5, May 16, 2025

  ABSTRACT: Using Hirota’s bilinear derivative method to derive single-breather solutions for the modified nonlinear Schrödinger (MNLS) equation and the derivative nonlinear Schrödinger (DNLS) equation under non-vanishing boundary conditions, along with explicit mixed solutions combining breather-type and pure solitons. The collision dynamics between pure and breather-type solitons in a mixed solution has been graphically demonstrated and analyzed. Furthermore, by setting specific parameter to zero, we naturally obtain corresponding single-breather solution and its explicit mixed solutions with pure solitons for the DNLS equation. The mixed soliton solution can asymptotically degenerate into a simple algebraic summation of a simple pure soliton and a breather in the infinite past or the infinite future, which was graphically validated.