1995/09/13 by P. G. Grinevich, Grinevich, P. G.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.solv-int/9509004
openalex publication_date 1995/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In our paper we construct a new infinite family of symmetries of the Whitham equations (averaged Korteveg-de-Vries equation). In contrast with the ordinary hydrodynamic-type flows these symmetries are nonhomogeneous (i.e. they act nontrivially at the constant solutions), are nonlocal, explicitly depend upon space and time coordinates and form a noncommutative algebra, isomorphic to the algebra of the polynomial vector fields in the complex plane (Virasoro algebra with the zero central charge).