Title: Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrodinger equation: far-field behavior
Speaker: Prof. Dengshan Wang ( Beijing Normal University )
Time: 2021-4-2 (Friday) 18:00
Tencent Conference :
Conference ID：786 276 354
Password: 1234
Inviter: Tiecheng Xia
Abstract: The integrable focusing NLS equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We study families of such multiple-pole solitons generated by Darboux transformations as the pole order tends to infinity. It is shown that in an appropriate scaling, there are four regions in the space-time plane: an exponential-decay region, an algebraic-decay region, a non-oscillatory region, and an oscillatory region. Using the nonlinear steepest-descent method for analyzing Riemann-Hilbert problems, we compute the leading-order asymptotic behavior in the algebraic-decay, non-oscillatory, and oscillatory regions, respectively. This is a joint work with D. Bilman and R. Buckingham [arXiv:1911.04327v1]. Finally, we briefly introduce our recent work on the multiple-pole solitons in the focusing mKdV equation.