2002/04/25 by V. S. Shchesnovich, Valery S. Shchesnovich, Jianke Yang +2 · 8 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebraic number #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical analysis #Mathematics #Multiplicity (mathematics) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Order (exchange) #Pattern Formation and Solitons (nlin.PS) #Physics #Quantum electrodynamics #Quantum mechanics #Soliton #nlin.PS #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0204058
published in arXiv (Cornell University) (Cornell University) · Revised version; 33 pages; 5 figures; to appear in Studies of Applied Mathematics
openalex publication_date 2002/04/25 · arxiv created 2002/08/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The soliton dressing matrices for the higher-order zeros of the Riemann-Hilbert problem for the N-wave system are considered. For the elementary higher-order zero, i.e. whose algebraic multiplicity is arbitrary but the geometric multiplicity is 1, the general soliton dressing matrix is derived. The theory is applied to the study of higher-order soliton solutions in the three-wave interaction model. The simplest higher-order soliton solution is presented. In the generic case, this solution describes the breakup of a higher-order pumping wave into two higher-order elementary waves, and the reverse process. In non-generic cases, this solution could describe (i) the merger of a pumping sech wave and an elementary sech wave into two elementary waves (one sech and the other one higher-order); (ii) the breakup of a higher-order pumping wave into two elementary sech waves and one pumping sech wave; and the reverse processes. This solution could also reproduce fundamental soliton solutions as a special case.