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The peculiar intergrability of the Davey-Stewartson equation allows us to find analytically solutions describing the simultaneous formation and interaction of one-dimensional and two-dimensional localized coherent structures. The predicted phenomenology allows us to address the issue of interaction of solitons of different dimensionality that may serve as a starting point for the understanding of hybrido-dimensional collisions recently observed in nonlinear optical media.
We present experimental evidence of the universal emergence of the Peregrine soliton predicted in the semi-classical (zero-dispersion) limit of the focusing nonlinear Schr{o}dinger equation [Comm. Pure Appl. Math. {bf 66}, 678 (2012)]. Experiments st
The generalized perturbative reduction method is used to find the two-component vector breather solution of the Born-Infeld equation $ U_{tt} -C U_{zz} = - A U_{t}^{2} U_{zz} - sigma U_{z}^{ 2} U_{tt} + B U_{z} U_{t} U_{zt} $. It is shown that the so
We study coupled unstaggered-staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schr{o}dinger (DNLS) equations with the self-attractive on-site self-phase-modulation nonlinearity, coupled by the repulsive cross-phase-mod
We reveal intrinsic topological vector potentials underlying the nonlinear waves governed by one-dimensional nonlinear Schr{o}dinger equations by investigating the Berry connection of the linearized Bogoliubov-de-Gennes (BdG) equations in an extended
We study numerically the integrable turbulence developing from strongly nonlinear partially coherent waves, in the framework of the focusing one-dimensional nonlinear Schrodinger equation. We find that shortly after the beginning of motion the turbul