Journal of High Energy Physics

, 2016:8 | Cite as

Regularized degenerate multi-solitons

  • Francisco Correa
  • Andreas FringEmail author
Open Access
Regular Article - Theoretical Physics


We report complex \( \mathcal{P}\mathcal{T} \)-symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these solutions originate from degenerate energy solutions of the Schrödinger equation. Technically this is achieved by the application of Darboux-Crum transformations involving Jordan states with suitable regularizing shifts. Alternatively they may be constructed from a limiting process within the context Hirota’s direct method or on a nonlinear superposition obtained from multiple Bäcklund transformations. The proposed procedure is completely generic and also applicable to other types of nonlinear integrable systems.


Integrable Field Theories Integrable Hierarchies Space-Time Symmetries 


Open Access

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Instituto de Ciencias Físicas y MatemáticasUniversidad Austral de ChileValdiviaChile
  2. 2.Institut für Theoretische Physik and Riemann Center for Geometry and PhysicsLeibniz Universität HannoverHannoverGermany
  3. 3.Department of MathematicsCity University LondonLondonU.K.

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