The solution of the global relation for the derivative nonlinear Schrodinger equation on the half-line
2011 (English)In: Physica D: Non-linear phenomena, ISSN 0167-2789, Vol. 240, no 6, 512-525 p.Article in journal (Refereed) Published
We consider initial-boundary value problems for the derivative nonlinear Schrdinger (DNLS) equation on the half-line x>0. In a previous work, we showed that the solution q(x,t) can be expressed in terms of the solution of a RiemannHilbert problem with jump condition specified by the initial and boundary values of q(x,t). However, for a well-posed problem, only part of the boundary values can be prescribed; the remaining boundary data cannot be independently specified, but are determined by the so-called global relation. In general, an effective solution of the problem therefore requires solving the global relation. Here, we present the solution of the global relation in terms of the solution of a system of nonlinear integral equations. This also provides a construction of the Dirichlet-to-Neumann map for the DNLS equation on the half-line.
Place, publisher, year, edition, pages
2011. Vol. 240, no 6, 512-525 p.
Derivative nonlinear Schrdinger equation, Dirichlet-to-Neumann map, Initial-boundary value problem, Integrable system, Boundary data, Boundary values, DNLS equation, Effective solution, Half-line, Initial-boundary value problems, Integrable systems, Jump conditions, Nonlinear integral equations, Riemann Hilbert problems, Schrdinger equations, Well-posed problems, Initial value problems, Integral equations, Ordinary differential equations, Nonlinear equations
Physical Sciences Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-163812DOI: 10.1016/j.physd.2010.11.004ISI: 000287386600005ScopusID: 2-s2.0-78751571215OAI: oai:DiVA.org:kth-163812DiVA: diva2:802382
QC 201504272015-04-132015-04-122015-04-27Bibliographically approved