Coupled derivative nonlinear Schrödinger III equation: Darboux transformation and higher-order rogue waves in a two-mode nonlinear fiber. (English) Zbl 1510.35318
Summary: The coupled derivative nonlinear Schrödinger III (cDNLSIII) equation describes pulse propagations in a two-mode nonlinear fiber. In this paper, we construct the \(N\)-fold generalized Darboux transformation (DT) with the limit approach, from which the general higher-order rogue wave solutions of the cDNLSIII equation are obtained. These solutions, divided into three categories, namely, rogue waves and rogue waves on multi-soliton and multi-breather backgrounds, have applications in nonlinear fiber communication. Furthermore, we present some interesting interactions between rogue waves and solitons or breathers and analyze the features of each type.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35C08 | Soliton solutions |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
Keywords:
coupled derivative nonlinear Schrödinger III equation; \(N\)-fold generalized Darboux transformation; multi-soliton and multi-breather; higher-order rogue wavesReferences:
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