Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method

  • Micheline Musette
Part of the Lecture Notes in Physics book series (LNP, volume 632)


We study by the singular manifold method a few 1+1-dimensional partial differential equations which possess N-soliton solutions for arbitrary N, i.e. classes of solutions particularly stable under the nonlinear interaction. The existence of such solutions represents one of the different aspects of the property of integrability, and it can be connected to the existence of a Bäcklund transformation from which a nonlinear superposition formula can be established.


Laurent Series Darboux Transformation Order Linear Equation Moutard Transformation Acklund Transformation 
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Authors and Affiliations

  • Micheline Musette
    • 1
  1. 1.Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 BrusselsBelgium

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