Abstract
We consider large-scale dynamics of non-equilibrium dense soliton gas for the Korteweg-de Vries (KdV) equation in the special ``condensate'' limit. We prove that in this limit the integro-differential kinetic equation for the spectral density of states reduces to the $N$-phase KdV-Whitham modulation equations derived by Flaschka, Forest and McLaughlin (1980) and Lax and Levermore (1983). We consider Riemann problems for soliton condensates and construct explicit solutions of the kinetic equation describing generalized rarefaction and dispersive shock waves. We then present numerical results for "diluted'' soliton condensates exhibiting rich incoherent behaviors associated with integrable turbulence.
Original language | English |
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Article number | 104 |
Number of pages | 45 |
Journal | Journal of Nonlinear Science |
Volume | 33 |
Issue number | 6 |
DOIs | |
Publication status | Published - 19 Sept 2023 |
Keywords
- Integrability
- Kinetic equation
- Korteweg-de Vries equation
- Soliton gas
- Whitham modulation equations