13 citations · 24 across the 5 of their papers we have counts for
5 papers
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 ellipti…
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 init…
On the Cauchy problem of defocusing mKdV equation with finite density initial data: long time asymptotics in soliton-less regions
Taiyang Xu, Zechuan Zhang, Engui Fan
We investigate the long-time asymptotics for the solutions to the Cauchy problem of defocusing modified Kortweg-de Vries (mKdV) equation with finite density initial data. The prese…
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…
Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov-Ivanov equation under the zero/nonzero background
Zhang Zechuan, Fan Engui
In this article, the inverse scattering transform is considered for the Gerdjikov-Ivanov equation with zero and non-zero boundary conditions by a matrix Riemann-Hilbert (RH) method…