On integrability of a new dynamical system associated with the BBM-type hydrodynamic flow

Autor:	Dutykh, Denys, Prykarpatskyy, Yarema A.
Rok vydání:	2024
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematical Physics Mathematics - Analysis of PDEs Nonlinear Sciences - Pattern Formation and Solitons 58J70 37J35 (primary) 76B15 35A30 37K35 (secondary)
Druh dokumentu:	Working Paper
Popis:	This article explores the exceptional integrability property of a family of higher-order Benjamin-Bona-Mahony (BBM)-type nonlinear dispersive equations. Here, we highlight its deep relationship with a generalized infinite hierarchy of the integrable Riemann-type hydrodynamic equations. A previous Lie symmetry analysis revealed a particular case which was conjectured to be integrable. Namely, a Lie-Baecklund symmetry exists, thus highlighting another associated dynamical system. Here, we investigate these two equations using the gradient-holonomic integrability scheme. Moreover, we construct their infinite hierarchy of conservation laws analytically, using three compatible Poisson structures to prove the complete integrability of both dynamical systems. We investigate these two equations using the so-called gradient-holonomic integrability scheme. Based on this scheme, applied to the equation under consideration, we have analytically constructed its infinite hierarchy of conservation laws, derived two compatible Poisson structures and proved its complete integrability. Comment: 21 pages, 4 figures, 33 references
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.07900 Zobrazit plný text záznamu View this record from Arxiv