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.