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Pelloni, B. (2000) Initial boundary value problems for the nonlinear Schrödinger equation. Theoretical and Mathematical Physics, 122 (1). pp. 107-120. ISSN 0040-5779 doi: 10.1007/BF02551174
Abstract/Summary
A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.
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| Item Type | Article |
| URI | https://reading-clone.eprints-hosting.org/id/eprint/7543 |
| Item Type | Article |
| Refereed | Yes |
| Divisions | Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics |
| Publisher | Springer Verlag |
| Download/View statistics | View download statistics for this item |
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