2024/06/19 by Denys Dutykh, Dutykh, Denys, Yarema A. Prykarpatskyy +1
Engineering · Physics and Astronomy · #35A30 #37J35 (primary) #37K35 (secondary) #58J70 #76B15 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2407.07900
openalex publication_date 2024/06/19 · openalex created_date 2024/07/14 · openalex updated_date 2026/07/28
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.