School of Mathematical & Statistical Sciences Faculty Publications

Darboux Transformation and General Soliton Molecule Pairs for a Generalized Reverse Space Nonlinear Schrödinger Equation

Document Type

Article

Publication Date

6-17-2026

Abstract

The generalized reverse space nonlinear Schrödinger (NLS) equation, which can be derived from the parity-symmetric reduction of the Manakov system, is studied by the Darboux transformation (DT) method. To ensure the target equation’s integrability, we present both Lax pair and infinitely-many conservation laws. Starting from the two-fold DT, we reduce it to fulfill two symmetry conditions for the Lax pair, ultimately yield the N-step DT for the equation in a compact determinant form. As an application, the general L-soliton molecule pair-(N−L)-soliton solutions (2≤L≤N), which include the soliton molecule pairs formed by arbitrary L soliton pairs and the common (N−L) soliton pairs, are successfully obtained through our resulted DT. Furthermore, the general soliton molecule pairs can be reduced to N-soliton pairs, pure soliton molecule pairs, and their interactions. Particularly, the one-soliton pair solution is verified to admit the interactions between two head-on solitons. Finally, the generation mechanism and dynamics of the soliton molecule pairs are all discussed in detail.

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Publication Title

Qualitative Theory of Dynamical Systems

DOI

10.1007/s12346-026-01536-7

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