Critical density of a soliton gas

Abstract

We quantify the notion of a dense soliton gas by establishing an upper bound for the integrated density of states of the quantum-mechanical Schrödinger operator associated with the KdV soliton gas dynamics. As a by-product of our derivation we find the speed of sound in the soliton gas with Gaussian spectral distribution function.

7 pages

References in corpus (3)

• Soliton Turbulence in Shallow Water Ocean Surface Waves
• Transitions From Order to Disorder in Multi-Dark and Multi-Dark-Bright Soliton Atomic Clouds
• Non-periodic one-gap potentials in quantum mechanics

Cited by in corpus (13)

• Soliton gas in integrable dispersive hydrodynamics
• Experimental evidence of a hydrodynamic soliton gas
• Spectral theory of soliton and breather gases for the focusing nonlinear Schrödinger equation
• Rigorous asymptotics of a KdV soliton gas
• Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modeling
• Soliton gas in bidirectional dispersive hydrodynamics
• Almost Periodicity in Time of Solutions of the KdV Equation
• Soliton spectra of random water waves in shallow basins
• KdV equation beyond standard assumptions on initial data
• Statistical properties of extreme soliton collisions
• Bound-state soliton gas as a limit of adiabatically growing integrable turbulence
• Properties of synchronous collisions of solitons in the Korteweg - de Vries equation
• Dynamics of Interaction of Two Soliton Clouds