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I will report my recent joint work with Jacek Jendrej on muti-solitons to the Klein-Gordon equations including their asymptotic stability and classification.
In this talk we review some recent results on the multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schr鰀inger equations. We will show the corresponding construction and co...
In this talk we review some recent results on the multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schr鰀inger equations. We will show the corresponding construction and co...
Peaked soliton dynamics is one of the most intriguing features of the Camassa-Holm-type integrable equations. In this talk, I will give a review on the issue of the stability of peaked solitons, inclu...
Peaked soliton dynamics is one of the most intriguing features of the Camassa-Holm-type integrable equations. In this talk, I will give a review on the issue of the stability of peaked solitons, inclu...
We show that the “instantonic” soliton of five-dimensional Yang-Mills theory and the closely related BPS monopole of four-dimensional Yang-Mills/Higgs theory continue to be exact static, and stable, s...
I consider electrodynamics and the problem of knotted solitons in two-component superconductors. Possible existence of knotted solitons in multicomponent superconductors was predicted several years ag...
This dissertation focuses on the properties of nonlinear waves in Bose-Einstein condensates (BECs). The fundamental model here is the nonlinear Schrodinger equation, the so-called Gross-Pitaevskii (GP...
In this report, fundamental educational concepts of linear and non-linear equations and solutions of nonlinear equations from the book High-Temperature Superconductivity: The Nonlinear Mechanism and T...
We study two-component solitons and their symmetry-breaking bifurcations (SBBs) in linearly coupled photonic systems with a spatially inhomogeneous strength of the coupling. One system models an inver...
We demonstrate theoretically and experimentally that the transverse instability of coherent soliton stripes can be greatly suppressed or totally eliminated when the soliton stripes propagate in a one-...
We study inelastic collisions of counter-propagating self-induced transparency solitons in a homogeneously broadened two-level medium. The energy of the pulse can be almost totally absorbed in the med...
We theoretically investigate the stability and dynamics of self-channelled beams that form via nonlocal optomechanical interactions in dual-nanoweb microstructured fibers. These "optomechanicons" repr...
Abstract: In this paper, we obtain stable and metastable soliton solutions of a coupled system of two real scalar fields with five five discrete points of vacua. These solutions have definite topologi...
Abstract: Inter-site interactions play a crucial role in polar gases in optical lattices even in the absence of hopping. We show that due to these long-range interactions a destabilized stack of quasi...

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