On the Inverse Scattering Method for Integrable PDEs on a Star Graph

Caudrelier, V. (2015). On the Inverse Scattering Method for Integrable PDEs on a Star Graph. Communications in Mathematical Physics, 338(2), pp. 893-917. doi: 10.1007/s00220-015-2378-9

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Abstract

© 2015, Springer-Verlag Berlin Heidelberg. We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary value (IBV) problem and then to extend the unified method of Fokas to such a matrix IBV problem. The nonlinear Schrödinger equation is chosen to illustrate the method. The framework unifies all previously known examples which are recovered as particular cases. The case of general Robin conditions at the vertex is discussed: the notion of linearizable initial-boundary conditions is introduced. For such conditions, the method is shown to be as efficient as the ISM on the full-line.

Item Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-015-2378-9
Uncontrolled Keywords: inverse scattering method, star-graph, integrable PDE, unified Fokas method, nonlinear Schr¨odinger equation
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/11946

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