Dispersionless (3+1)-dimensional integrable hierarchies
نویسندگان
چکیده
منابع مشابه
Symmetries and tau function of higher dimensional dispersionless integrable hierarchies
A higher dimensional analogue of the dispersionless KP hierarchy is introduced. In addition to the two-dimensional “phase space” variables (k, x) of the dispersionless KP hierarchy, this hierarchy has extra spatial dimensions compactified to a two (or any even) dimensional torus. Integrability of this hierarchy and the existence of an infinite dimensional of “additional symmetries” are ensured ...
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The notion of string equations was discovered in the end of the eighties, and has been studied in the language of integrable hierarchies. String equations in the KP hierarchy are nowadays relatively well understood. Meanwhile, systematic studies of string equations in the Toda hierarchy started rather recently. This article presents the state of art of these issues from the author’s point of vi...
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We show that conformal maps of simply connected domains with an analytic boundary to a unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The maps are determined by a particular solution to the hierarchy singled out by the conditions known as ”string equations”. The same hierarchy locally solves the 2D inverse potential problem, i.e., reconstruction of the d...
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The quasi-classical ∂̄-dressing method is used to derive compact generating equations for dispersionless hierarchies. Dispersionless Kadomtsev-Petviashvili (KP) and two-dimensional Toda lattice (2DTL) hierarchies are considered as illustrative examples.
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The paper is an inquiry of the algebraic foundations of the theory of dispersionless integrable hierarchies, like the dispersionless KP and modified KP hierarchies and the universal Whitham’s hierarchy of genus zero. It stands out for the idea of interpreting these hierarchies as equations of coisotropic deformations for the structure constants of certain associative algebras. It discusses the ...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2017
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2016.0857