Communications in Mathematical Physics

, Volume 338, Issue 2, pp 893–917 | Cite as

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

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Abstract

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.

Keywords

Soliton Hilbert Problem Robin Boundary Condition Star Graph Integrable Boundary Condition 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsCity University LondonLondonUK

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