2018/09/03 by Cheng Zhang, Zhang, Cheng
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.48550/arxiv.1809.00432
21 pages, 10 figures, correcting typos of the previous upload
openalex publication_date 2018/09/03 · arxiv created 2018/09/05 · arxiv updated 2018/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Based on the theory of integrable boundary conditions (BCs) developed by Sklyanin, we provide a direct method for computing soliton solutions of the focusing nonlinear Schrödinger (NLS) equation on the half-line. The integrable BCs at the origin are represented by constraints of the Lax pair, and our method lies on dressing the Lax pair by preserving those constraints in the Darboux-dressing process. The method is applied to two classes of solutions: solitons vanishing at infinity and self-modulated solitons on a constant background. Half-line solitons in both cases are explicitly computed. In particular, the boundary-bound solitons, that are static solitons bounded at the origin, are also constructed. We give a natural inverse scattering transform interpretation of the method as evolution of the scattering data determined by the integrable BCs in space.