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Kaup, D.J. and Newell, A.C. (1978) Solitons as Particles, Oscillators, and in Slowly Changing Media: A Singular Perturbation Theory. Proceedings of the Royal Society of London, series A, 361, 413-446.

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.