2024/03/29 by Pierandrea Vergallo, Vergallo, Pierandrea, E. V. Ferapontov +1 · 1 citation
Mathematics · Physics and Astronomy · #Gas Dynamics and Kinetic Theory #Optical properties and cooling technologies in crystalline materials #Cold Atom Physics and Bose-Einstein Condensates
paper · pdf · doi:10.48550/arxiv.2403.20162
We investigate Hamiltonian aspects of the integro-differential kinetic equation for dense soliton gas which results as a thermodynamic limit of the Whitham equations. Under a delta-functional ansatz, the kinetic equation reduces to a non-diagonalisable system of hydrodynamic type whose matrix consists of several 2× 2 Jordan blocks. We demonstrate that the resulting system possesses local Hamiltonian structures of differential-geometric type, for all standard two-soliton interaction kernels (KdV, sinh-Gordon, hard-rod, Lieb-Liniger, DNLS, and separable cases). In the hard-rod case, we show that the continuum limit of these structures provides a local multi-Hamiltonian formulation of the full kinetic equation.