City Research Online

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 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.

Publication Type:	Article
Additional Information:	Perturbative QCD, Renormalization Group, Resummation, Effective field theories
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Engineering
SWORD Depositor:	Symplectic Administrator

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