By means of the Darboux transformation, we obtain analytical solutions for a soliton set on top of a plane-wave background in coupled Gross-Pitaevskii equations describing a binary Bose-Einstein condensate. We consider basic properties of the solutions with and without the cross interaction [cross phase modulation (XPM)] between the two components of the background. In the absence of the XPM, t...

We point out that a common feature of integrable hierarchies presenting soliton solutions is the existence of some special “vacuum solutions” such that the Lax operators evaluated on them, lie in some abelian subalgebra of the associated Kac-Moody algebra. The soliton solutions are constructed out of those “vacuum solitons” by the dressing transformation procedure. This talk is concerned with t...

Pulse broadening for optical solitons due to birefringence is investigated. We present an analytical solution which describes the propagation of solitons in birefringent optical fibers. The special solutions consist of a combination of purely solitonic terms propagating along the principal birefringence axes and soliton-soliton interaction terms. The solitonic part of the solutions indicates th...

Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete versions Abstract. We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable s...

We have found a new class of exact solutions for multicomponent partially coherent solitons in photorefractive media with a drift mechanism of nonlinear response. Their novel feature is that the composite M-component sech-shaped soliton is located on a constant-background plane wave. The solutions are characterized by two free parameters and these are related to the maximum intensity of the com...

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable yaverage trick (which is usually adopted in literature) is removed. The derived models are classified via Painlevé test. Three types of τ -function solutions and multiple soliton solutions of the models are explicitly given by means of the exact ...

We study infinite soliton trains solutions of nonlinear Schrödinger equations, i.e. solutions behaving as the sum of infinitely many solitary waves at large time. Assuming the composing solitons have sufficiently large relative speeds, we prove the existence and uniqueness of such a soliton train. We also give a new construction of multi-solitons (i.e. finite trains) and prove uniqueness in an ...