Superposition of the coupled NLS and MKdV systems

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GÜRSES M., Pekcan A.

APPLIED MATHEMATICS LETTERS, vol.98, pp.157-163, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 98
  • Publication Date: 2019
  • Doi Number: 10.1016/j.aml.2019.06.002
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.157-163
  • Keywords: Hirota equations, Superposition of integrable equations, Ablowitz-Musslimani reduction, Hirota bilinear method, Soliton solutions, NONLINEAR SCHRODINGER-EQUATION, INVERSE SCATTERING TRANSFORM, DE-VRIES EQUATION, SOLITON-SOLUTIONS
  • Hacettepe University Affiliated: Yes


Superpositions of hierarchies of integrable equations are also integrable. The superposed equations, such as the Hirota equations in the AKNS hierarchy, cannot be considered as new integrable equations. Furthermore if one applies the Hirota bilinear method to these equations one obtains the same N-soliton solutions of the generating equation which differ only by the dispersion relations. Similar discussions can be made for the locally and nonlocally reduced equations as well. We give, as an example, AKNS system of equations in (1 + 1)-dimensions. (C) 2019 Elsevier Ltd. All rights reserved.