Quasi-classical -dressing approach to the weakly dispersive KP hierarchy

Konopelchenko, Boris and Moro, Antonio (2003) Quasi-classical -dressing approach to the weakly dispersive KP hierarchy. Journal of Physics A: Mathematical and General, 36 (47). pp. 11837-11851. ISSN 0305-4470

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Abstract

The recently proposed quasi-classical \bar{\partial} -dressing method provides a systematic approach to studying the weakly dispersive limit of integrable systems. We apply the quasi-classical \bar{\partial} -dressing method to describe dispersive corrections of any order. We show how to calculate the \bar{\partial} problems at any order for a rather general class of integrable systems, presenting explicit results for the KP hierarchy case. We demonstrate the stability of the method at each order. We construct an infinite set of commuting flows at first order which allows a description analogous to the zero-order (purely dispersionless) case, highlighting a Whitham-type structure. Obstacles for the construction of the higher order dispersive corrections are also discussed.

Item Type:	Article
Subjects:	F300 Physics
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Becky Skoyles
Date Deposited:	17 Jul 2018 11:39
Last Modified:	11 Oct 2019 19:45
URI:	http://nrl.northumbria.ac.uk/id/eprint/35029

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