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Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
In the second part, I will mainly focus on two semi-discrete models: Ablowitz-Ladik equation and fully discrete NLS equation. First, I will clarify the connection of these two discrete models with dis...
In these two talks, I will present a unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach. I will take the NLS equation as a typical example and show h...
Consider to the Cauchy problem of the defocusing NLS equation with a nonzero background. With the Dbar generalization of the nonlinear steepest descent method to compute the leading order approximatio...
The talk is about applications of bilinear approaches to N-soliton solutions in (2+1)-dimensions. The Hirota N-soliton condition will be analyzed, together with novel examples of (2+1)-dimensional sol...
We will talk about the Hirota direct method and its applications to soliton solutions in (1+1)-dimensions. Both known and new examples of soliton equations will be discussed, and generalized bilinear ...
We study confined solutions of certain evolutionary partial differential equations (PDE) in 1 + 1 space–time. The PDE we study are Lie–Poisson Hamiltonian systems for quadratic Hamiltonians defined on...
Isometric immersions of space forms and soliton theory.
We examine collisions between identical solitons in a weakly perturbed Ablowitz-Ladik (AL) model, augmented by either onsite cubic nonlinearity (which corresponds to the Salerno model, and may be real...
While fundamental-mode discrete solitons have been demonstrated with both self-focusing and defocusing nonlinearity, high-order-mode localized states in waveguide lattices have been studied thus far o...
We investigate bright matter-wave solitons in the presence of a spatially varying nonlinearity. It is demonstrated that a translation mode is excited due to the spatial inhomogeneity and its frequency...
We consider vector solitons of mixed bright-dark types in quasi-one-dimensional spinor (F=1) Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrabl...
We revisit the problem of the three-soliton collisions in the weakly perturbed sine-Gordon equation and develop an effective three-particle model allowing us to explain many interesting features obser...
We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schrödinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic fiel...
We report the numerical realization of robust two-component structures in 2D and 3D Bose-Einstein condensates with nontrivial topological charge in one component. We identify a stable symbiotic state ...

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