We review the different dynamical mechanisms leading to the emergence of coherent
structures in physical systems described by the integrable one-dimensional nonlinear …

The long-time asymptotics of the focusing Kundu–Eckhaus equation with nonzero boundary
conditions at infinity is investigated by the nonlinear steepest descent method of Deift and …

There is growing physical and mathematical interest in the hydrodynamics of
dissipationless/dispersive media. Since GB Whitham's seminal publication fifty years ago …

In optical fibres, weak modulations can grow at the expense of a strong pump to form a
triangular comb of sideband pairs, until the process is reversed. Repeated cycles of such …

We investigate the fundamental phenomenon of the spontaneous, noise-induced
modulational instability (MI) of a plane wave. The statistical properties of the noise-induced …

We report experimental confirmation of the universal emergence of the Peregrine soliton
predicted to occur during pulse propagation in the semiclassical limit of the focusing …

It is shown how to compute the instability rates for the double-periodic solutions to the cubic
NLS (nonlinear Schrödinger) equation by using the Lax linear equations. The wave function …

We study the dynamics of Kuznetsov-Ma solitons (KMSs) in the framework of vector
nonlinear Schrödinger (Manakov) equations. An exact multiparameter family of solutions for …

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 study the nonlinear stage of modulational
instability of a plane wave in the presence of a localized perturbation. Using a recirculating …