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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...
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...
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...
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: Motivated by M\"obius transformation for symmetrical points under the generalized circle in complex plane, the system of symmetrical spin coherent states corresponding to antipodal qubit sta...
Abstract: We present new solutions in terms of elementary functions of the multi-component nonlinear Schr\"odinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton...
We study soliton oscillations in a trapped superfluid Fermi gas across the Bose-Einstein conden-sate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. We derive an exact equation relating the phase ju...
It is demonstrated the existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with linear OL in the $x-$direction and nonlinear OL (NOL) in the $y-$direction, where the ...
Exact solutions for the generalized nonlinear Schr\"odinger (NLS) equation with inhomogeneous complex linear and nonlinear potentials are found. We have found localized and periodic solutions for a w...
The analytical theory of chirped dissipative soliton solutions of nonlinear complex Ginzburg-Landau equation is exposed. Obtained approximate solutions are easily traceable within an extremely broad r...
We study the stability of multipole-mode solitons in one-dimensional thermal nonlinear media. We show how the sample geometry impacts the stability of mutlipole-mode solitons and reveal that the tripo...

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