2022/05/28 by Liming Ling, Ling, Liming, Xiaoen Zhang +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.MP #msc:35Q15 #msc:35Q51 #msc:35Q55 #msc:37K10 #msc:37K15 #msc:37K40 #nlin.SI
paper · pdf · doi:10.48550/arxiv.2205.14359
47pages
arxiv created 2022/05/28 · arxiv updated 2022/05/31
Multi-soliton and high-order soliton solutions are two type of famous ones in the integrable focusing nonlinear Schrödinger equation. The dynamics of multi-soliton was well known to us since 70s of the last century by the determinant analysis. However, there is few progress on the high-order solitons. In this work, we would like to analyze the large order asymptotics for the high-order breathers, which are special cases of double high-order solitons with the same velocity to the nonlinear Schrödinger equation. To analyze the large order dynamics, we first convert the representation of Darboux transformation into a framework of Riemann-Hilbert problem. Then we show that there exist five distinct asymptotic regions by the Deift-Zhou nonlinear steepest descent method. It is very interesting that a novel genus-three asymptotic region is first found in the large order asymptotics to large high-order breathers, which enriches the dynamic behaviors in the field of large order solitons. All results to the asymptotic analysis are verified by the numerical method.