[HTML][HTML] Long-time asymptotics of the focusing Kundu–Eckhaus equation with nonzero boundary conditions
DS Wang, B Guo, X Wang - Journal of Differential Equations, 2019 - Elsevier
The long-time asymptotics of the focusing Kundu–Eckhaus equation with nonzero boundary
conditions at infinity is investigated by the nonlinear steepest descent method of Deift and …
conditions at infinity is investigated by the nonlinear steepest descent method of Deift and …
Long-time asymptotics for the spin-1 Gross–Pitaevskii equation
X Geng, K Wang, M Chen - Communications in Mathematical Physics, 2021 - Springer
On the basis of the spectral analysis of the 4 * 4 4× 4 Lax pair associated with the spin-1
Gross–Pitaevskii equation and the scattering matrix, the solution to the Cauchy problem of …
Gross–Pitaevskii equation and the scattering matrix, the solution to the Cauchy problem of …
On the long-time asymptotics of the modified Camassa-Holm equation in space-time solitonic regions
Y Yang, E Fan - Advances in Mathematics, 2022 - Elsevier
We study the long time asymptotic behavior for the Cauchy problem of the modified
Camassa-Holm (mCH) equation in the solitonic regions m t+(m (u 2− ux 2)) x+ κ ux= 0, m …
Camassa-Holm (mCH) equation in the solitonic regions m t+(m (u 2− ux 2)) x+ κ ux= 0, m …
Long-time asymptotic behavior for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equation with time-periodic boundary condition
SF Tian, TT Zhang - Proceedings of the American Mathematical Society, 2018 - ams.org
The Gerdjikov-Ivanov (GI) type of derivative nonlinear Schrödinger equation is considered
on the quarter plane whose initial data vanish at infinity while boundary data are time …
on the quarter plane whose initial data vanish at infinity while boundary data are time …
Rigorous analysis of the unified transform method and long-range instabilities for the inhomogeneous time-dependent Schrödinger equation on the quarter-plane
A Chatziafratis, T Ozawa, SF Tian - Mathematische Annalen, 2024 - Springer
In this paper, we report on the discovery of a previously-unknown type of long-range
instability phenomenon for the one-dimensional linear Schrödinger (LS) equation on the …
instability phenomenon for the one-dimensional linear Schrödinger (LS) equation on the …
The unified method: I. Nonlinearizable problems on the half-line
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-
line can be analyzed by the unified method introduced by one of the authors and used …
line can be analyzed by the unified method introduced by one of the authors and used …
Long-time asymptotic for the derivative nonlinear Schrödinger equation with step-like initial value
J Xu, E Fan, Y Chen - Mathematical Physics, Analysis and Geometry, 2013 - Springer
We study long-time asymptotics of the solution to the Cauchy problem for the Gerdjikov-
Ivanov type derivative nonlinear Schrödinger equation iqt+ q xx− iq 2 q ̄ x+ 1 2| q| 4 q= 0 …
Ivanov type derivative nonlinear Schrödinger equation iqt+ q xx− iq 2 q ̄ x+ 1 2| q| 4 q= 0 …
The unified method: II. NLS on the half-line with t-periodic boundary conditions
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-
line can be analyzed by the unified method introduced by one of the authors and used …
line can be analyzed by the unified method introduced by one of the authors and used …
[HTML][HTML] Inverse scattering and N-triple-pole soliton and breather solutions of the focusing nonlinear Schrödinger hierarchy with nonzero boundary conditions
W Weng, Z Yan - Physics Letters A, 2021 - Elsevier
Based on the matrix Riemann-Hilbert problem we present the inverse scattering transform
for the focusing nonlinear Schrödinger (NLS) equation with nonzero boundary conditions …
for the focusing nonlinear Schrödinger (NLS) equation with nonzero boundary conditions …
[PDF][PDF] Long-time asymptotics for the Korteweg-de Vries equation with steplike initial data
arXiv:1210.7434v2 [nlin.SI] 10 Jun 2013 Page 1 arXiv:1210.7434v2 [nlin.SI] 10 Jun 2013
LONG-TIME ASYMPTOTICS FOR THE KORTEWEG–DE VRIES EQUATION WITH STEPLIKE …
LONG-TIME ASYMPTOTICS FOR THE KORTEWEG–DE VRIES EQUATION WITH STEPLIKE …