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Investigation of soliton equations with integral operators and their dynamics

We present Lax pairs and functions called Lax functions corresponding to Calogero- Moser-Sutherland (CMS) systems. We present the Benjamin-Ono (BO) equation and a pole ansatz to the BO equation, constructed from a specific type of Lax function called a special Lax function corresponding to Rational and Trigonometric CMS systems. We present a generalization of the BO equation called the non-chiral Intermediate wave (ncILW) equation and show that a family of solutions to the ncILW equation can be constructed from the special Lax function corresponding to the hyperbolic CMS system. We present the Szegö equation on the circle and the real line. We obtain a family of solutions to the Szegö equation on the real line using a pole ansatz. Using numerical methods, we display solution plots to the BO equation and Szegö equation.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-331110
Date January 2023
CreatorsVikars Hall, Ruben, Svennerstedt, Carl
PublisherKTH, Skolan för teknikvetenskap (SCI)
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/bachelorThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess
RelationTRITA-SCI-GRU ; 2023:154

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