The concept of soliton gas was introduced in 1971 by Zakharov as an infinite collection of
weakly interacting solitons in the framework of Korteweg–de Vries (KdV) equation. In this …

We report an optical fiber experiment in which we investigate the interaction between an
individual soliton and a dense soliton gas. We evidence a refraction phenomenon where the …

Using the Darboux transformation for the Korteweg–de Vries equation, we construct and
analyze exact solutions describing the interaction of a solitary wave and a traveling cnoidal …

The mathematical description of localized solitons in the presence of large‐scale waves is a
fundamental problem in nonlinear science, with applications in fluid dynamics, nonlinear …

We obtain Fredholm type formulas for partial degenerations of theta functions on
(irreducible) nodal curves of arbitrary genus, with emphasis on nodal curves of genus one …

Soliton gases represent large random soliton ensembles in physical systems that display
integrable dynamics at leading order. We report hydrodynamic experiments in which we …

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 …

We use Riemann problem for soliton gas as a benchmark for a detailed numerical validation
of the spectral kinetic theory for the Korteweg-de Vries (KdV) and the focusing nonlinear …

We study Jánossy densities of a randomly thinned Airy kernel determinantal point process.
We prove that they can be expressed in terms of solutions to the Stark and cylindrical …

This study explores multiple soliton and breather solutions on periodic backgrounds in the
complex modified Korteweg–de Vries equation. The compact determinant formulas and their …