Kinetic equation for a soliton gas and Its hydrodynamic reductions

DOI10.1007/s00332-010-9080-zzbMath1252.37056arXiv0802.1261OpenAlexW2098476508MaRDI QIDQ451125

J. Herrera, D. Rodríguez-Gómez

Publication date: 21 September 2012

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.1261

zbMATH Keywords

thermodynamic limitintegrabilitykinetic equationhydrodynamic reductionsoliton gas

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) First-order nonlinear hyperbolic equations (35L60) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (23)

Kinetic equation for soliton gas: integrable reductions ⋮ Generalized hydrodynamic reductions of the kinetic equation for a soliton gas ⋮ Critical density of a soliton gas ⋮ Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations ⋮ Generalized hydrodynamic limit for the box-ball system ⋮ Reductions of kinetic equations to finite component systems ⋮ Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation ⋮ Hamiltonian systems of Jordan block type: Delta-functional reductions of the kinetic equation for soliton gas ⋮ A continuous analog of the binary Darboux transformation for the Korteweg–de Vries equation ⋮ On classical integrability of the hydrodynamics of quantum integrable systems ⋮ A geometric viewpoint on generalized hydrodynamics ⋮ KdV equation beyond standard assumptions on initial data ⋮ Numerical simulation of a solitonic gas in KdV and KdV-BBM equations ⋮ Two-soliton interaction as an elementary act of soliton turbulence in integrable systems ⋮ Numerical modeling of soliton turbulence within the focusing Gardner equation: rogue wave emergence ⋮ Rigorous asymptotics of a KdV soliton gas ⋮ Rule 54: exactly solvable model of nonequilibrium statistical mechanics ⋮ Generalized hydrodynamics of the classical Toda system ⋮ Diffusion and superdiffusion from hydrodynamic projections ⋮ \(T\overline{T}\) deformations and the width of fundamental particles ⋮ Soliton gas in integrable dispersive hydrodynamics ⋮ Generalized hydrodynamics of the KdV soliton gas ⋮ Generalized hydrodynamics in box-ball system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Invariant integrability criterion for equations of hydrodynamic type
• On the Benney equations
• Collisionless Boltzmann equations and integrable moment equations
• Differential geometry of hydrodynamic Vlasov equations
• Hamiltonian formalism of weakly nonlinear hydrodynamic systems
• The rotation number for almost periodic potentials
• Method of averaging for two-dimensional integrable equations
• Tri-Hamiltonian structures of Egorov systems of hydrodynamic type
• The thermodynamic limit of the Whitham equations
• On the integrability of \((2+1)\)-dimensional quasilinear systems
• Conformal maps and reductions of the Benney equations
• Reductions of the Benney equations.
• Algebro-geometric approach in the theory of integrable hydrodynamic type systems
• Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor
• The continuum limit of theta functions
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• The small dispersion limit of the korteweg-de vries equation. ii
• The small dispersion limit of the Korteweg-de Vries equation. III
• The small dispersion limit of the Korteweg-de Vries equation. I
• Turbulence in Integrable Systems
• Spectral theory of two-dimensional periodic operators and its applications
• The korteweg-de vries equation with small dispersion: Higher order lax-levermore theory
• The Zero Dispersion Limit of the Korteweg-de Vries Equation With Periodic Initial Data
• Asymptotic Behavior of Stability Regions for Hill’s Equation
• The hyperbolic nature of the zero dispersion Kdv limit
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
• The zero dispersion limit, a deterministic analogue of turbulence
• The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type
• Multi-Hamiltonian structure of the Born–Infeld equation
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
• Unified approach to KdV modulations
• The generation, propagation, and extinction of multiphases in the KdV zero-dispersion limit
• Kinetic Equations and Integrable Hamiltonian Systems
• Some Properties of Long Nonlinear Waves
• Soliton turbulence as a thermodynamic limit of stochastic soliton lattices

This page was built for publication: Kinetic equation for a soliton gas and Its hydrodynamic reductions