3 papers
math.AP2026
Inverse scattering for the focusing nonlinear Schrödinger equation with elliptic background and full soliton gas
Tamara Grava, Robert Jenkins, Xiaofan Zhang +1
In this manuscript we develop the direct and inverse scattering problem for the cubic focusing nonlinear Schrödinger equation and for initial data that are asymptotic to an ellipt…
math.AP2026
Direct Scattering of the Focusing Nonlinear Schrödinger Equation with Step-like Oscillatory Initial Data
Tamara Grava, Robert Jenkins, Xiaofan Zhang +1
In this manuscript we set up the direct and inverse scattering problems for step-like traveling-wave solutions of the nonlinear Schrödinger equation. Specifically, we consider ini…
math.AP2025
Soliton resolution and asymptotic stability of -soliton solutions for the defocusing mKdV equation with a non-vanishing background
Zechuan Zhang, Taiyang Xu, Engui Fan
We analytically study the large-time asymptotics of the solution of the defocusing modified Korteweg-de Vries (mKdV) equation under a symmetric non-vanishing background, which supp…