Quasi-Periodic Solutions of the Universal Hierarchy

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Quasi-Periodic Solutions of the Universal Hierarchy

Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics. 2024.

We construct quasi-periodic solutions of the universal hierarchy which includes the multi-component KP and Toda hierarchies and show how they fit into the bilinear formalism. The tau-function is expressed in terms of the Riemann theta-function multiplied by exponential function of a quadratic form in the hierarchical times.

Research target: Mathematics

Language: English

DOI

Publication based on the results of:

Representation theory of vertex algebras and quantum groups with applications to knot theory, integrable systems, geometry of moduli spaces, and enumerative invariants (2024)

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In this paper, we revisit the classic problem of a wave field on a sloping beach of an arbitrary angle and propose a general approach that allows the computation of regular solutions of the problem regardless of the angle. We use the Mellin-transform technique, reducing the problem to singular integral equations with fixed-point singularities of ...

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The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...

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Suppose that ∆ ⊂ C is a domain, a function f is analytic in ∆, D = f(∆) is viewed as a Riemann surface. We put lR = {z ∈ ∆ : |f(z)| = R}. Let E ⊂ ∆ be a closed set. Put hα,β(r) = r α| ln r| β , 0 < α ...

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Bershtein M., Gavrylenko P., Marshakov A., Journal of High Energy Physics 2018 Vol. 08 No. 108 P. 1–54

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