Reflectionless Solutions for Square Matrix NLS with Vanishing Boundary Conditions

  • Francesco DemontisEmail author
  • Cornelis van der Mee


In this article we derive the reflectionless solutions of the 2 + 2 matrix NLS equation with vanishing boundary conditions and four different symmetries by using the matrix triplet method of representing the Marchenko integral kernel in separated form. Apart from using the Marchenko method, these solutions are also verified by direct substitution in the 2 + 2 NLS equation.


Matrix Nonlinear Schroedinger equation Inverse scattering transform Matrix triplets method Reflectionless solutions 

Mathematics Subject Classification (2010)

37K10 37K40 45Q05 



The research leading to this article has been partially supported by the Regione Autonoma della Sardegna in the framework of the research programs Integro-Differential equations and non-local problems and Algorithms and Models for Imaging Science [AMIS], and by INdAM-GNFM (Istituto Nazionale di Alta Matematica, National Institute of Advanced Mathematics – Gruppo Nazionale per la Fisica Matematica, National Group for Mathematical Physics).


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di CagliariCagliariItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità di CagliariCagliariItaly

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