Riemann-Hilbert approach for the integrable nonlocal nonlinear Schr\"odinger equation with step-like initial data
We study the Cauchy problem for the integrable nonlocal nonlinear Schr\"odinger (NNLS) equation \[ iq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\bar{q}(-x,t)=0 \] with a step-like initial data: $q(x,0)=o(1)$ as $x\to-\infty$ and $q(x,0)=A+o(1)$ as $x\to\infty$, where $A>0$ is an arbitrary constant. W...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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V.N. Karazin Kharkiv National University Publishing
2018-12-01
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| Series: | Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika |
| Subjects: | |
| Online Access: | https://periodicals.karazin.ua/mech_math/article/view/12134 |