Soliton gas in integrable dispersive hydrodynamics

Abstract

We review spectral theory of soliton gases in integrable dispersive hydrodynamic systems. We first present a phenomenological approach based on the consideration of phase shifts in pairwise soliton collisions and leading to the kinetic equation for a non-equilibrium soliton gas. Then a more detailed theory is presented in which soliton gas dynamics are modelled by a thermodynamic type limit of modulated finite-gap spectral solutions of the Korteweg-de Vries and the focusing nonlinear Schrödinger equations. For the focusing nonlinear Schrödinger equation the notions of soliton condensate and breather gas are introduced that are related to the phenomena of spontaneous modulational instability and the rogue wave formation. Integrability properties of the kinetic equation for soliton gas are discussed and some physically relevant solutions are presented and compared with direct numerical simulations of dispersive hydrodynamic systems.

59 pages, 18 figures

References in corpus (12)

• Soliton Turbulence in Shallow Water Ocean Surface Waves
• Experimental evidence of a hydrodynamic soliton gas
• Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation
• On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems
• Nonthermal fixed points and solitons in a one-dimensional Bose gas
• Solitons of the Resonant Nonlinear Schrodinger Equation with Nontrivial Boundary Conditions and Hirota Bilinear Method
• $T\bar{T}$-deformed conformal field theories out of equilibrium
• Dynamic soliton-mean flow interaction with nonconvex flux
• Persistence of hydrodynamic envelope solitons: detection and rogue wave occurrence
• Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation
• Hydrodynamic Equations for the Toda Lattice
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects

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• Form factors and generalized hydrodynamics for integrable systems
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• Hydrodynamic gauge fixing and higher order hydrodynamic expansion
• Soliton-mean field interaction in Korteweg-de Vries dispersive hydrodynamics
• Partial degeneration of finite gap solutions to the Korteweg-de Vries equation: soliton gas and scattering on elliptic background
• Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation
• Recent developments in spectral theory of the focusing NLS soliton and breather gases: the thermodynamic limit of average densities, fluxes and certain meromorphic differentials; periodic gases
• Observation of dense collisional soliton complexes in a two-component Bose-Einstein condensate
• The dissipative Generalized Hydrodynamic equations and their numerical solution
• Whitham Shocks and Resonant Dispersive Shock Waves Governed by the Higher Order Korteweg-de Vries Equation
• Benchmarks of Generalized Hydrodynamics for 1D Bose Gases
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