An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4x4 Lax pair on the half-line
Exactly Solvable and Integrable Systems
2017-06-07 v1 Mathematical Physics
Analysis of PDEs
math.MP
Quantum Physics
Abstract
We investigate the initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii (GP) equations with a 4x4 Lax pair on the half-line. The solution of this system can be obtained in terms of the solution of a 4x4 matrix Riemann-Hilbert (RH) problem formulated in the complex k-plane. The relevant jump matrices of the RH problem can be explicitly found using the two spectral functions s(k) and S(k), which can be defined by the initial data, the Dirichlet-Neumann boundary data at x=0. The global relation is established between the two dependent spectral functions. The general mappings between Dirichlet and Neumann boundary values are analyzed in terms of the global relation.
Keywords
Cite
@article{arxiv.1704.08534,
title = {An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4x4 Lax pair on the half-line},
author = {Zhenya Yan},
journal= {arXiv preprint arXiv:1704.08534},
year = {2017}
}
Comments
30 pages, 3 figures