Caudrelier, V. (2015). On the Inverse Scattering Method for Integrable PDEs on a Star Graph. Communications in Mathematical Physics, 338(2), pp. 893917. doi: 10.1007/s0022001523789

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Abstract
© 2015, SpringerVerlag Berlin Heidelberg. We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a stargraph. The idea is to map the problem on the graph to a matrix initialboundary 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 initialboundary conditions is introduced. For such conditions, the method is shown to be as efficient as the ISM on the fullline.
Item Type:  Article 

Additional Information:  The final publication is available at Springer via http://dx.doi.org/10.1007/s0022001523789 
Uncontrolled Keywords:  inverse scattering method, stargraph, 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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