Regularized degenerate multi-solitons

Abstract

We report complex PT-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 Schroedinger 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 Baecklund transformations. The proposed procedure is completely generic and also applicable to other types of nonlinear integrable systems.

15 pages, 4 figures

References in corpus (2)

• Making Sense of Non-Hermitian Hamiltonians
• PT-symmetric Deformations of the Korteweg-de Vries Equation

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• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• Multicomplex solitons
• Linearly stable and unstable complex soliton solutions with real energies in the Bullough-Dodd model
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• Non-Hermitian superintegrable systems
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models
• Hidden symmetries and nonlinear (super)algebras