Related papers: Knot soliton solutions for the one-dimensional non…
We consider a class of one dimensional vector Non-linear Schr$\ddot{o}$dinger Equation(NLSE) in an external complex potential with Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the components of the Schr$\ddot{o}$dinger field. The…
An inhomogeneous nonlinear Schr\"odinger equation is considered, that is invariant under $L^2$ scaling. The sharp condition for global existence of $H^1$ solutions is established, involving the $L^2$ norm of the ground state of the…
The paper studies existence of solutions for the nonlinear Schr\"odinger equation with a general bounded external magnetic field. In particular, no lattice periodicity of the magnetic field or presence of external electric field is…
A mapping between stationary solutions of nonlinear Sch\"odinger equations with real and complex potentials is constructed and a set of exact solutions with real energies are obtained for a large class of complex potentials. As specific…
In the paper an interaction between a soliton and a traveling wave in the Coupled Nonlinear Schr\"odinger Equation (CNLSE) is considered. The force acting on the soliton can both push or pull the soliton depending on parameters of the…
This work is concerned with the study of explicit solutions for a generalized coupled nonlinear Schr\"{o}dinger equations (NLS) system with variable coefficients. Indeed, we show, employing similarity transformations, the existence of Rogue…
A canonical variable coefficient nonlinear Schr\"{o}dinger equation with a four dimensional symmetry group containing $\SL(2,\mathbb{R})$ group as a subgroup is considered. This typical invariance is then used to transform by a symmetry…
The dynamics of soliton and quasisoliton solutions of cubic third order nonlinear Schr\"{o}dinger equation is studied. The regular solitons exist due to a balance between the nonlinear terms and (linear) third order dispersion; they are not…
We study the scattering of solitons in the nonlinear Schroedinger equation on local inhomogeneities which may give rise to resonant transmission and reflection. In both cases, we derive resonance conditions for the soliton's velocity. The…
In this work, we carry out a rigorous analysis of a multi-soliton solution of the focusing nonlinear Schr\"{o}dinger equation as the number, $N$, of solitons grows to infinity. We discover configurations of $N$-soliton solutions which…
In the present work we consider the subject of dark fractional solitary waves in the realm of generalized (fractional) forms of the nonlinear Schr\"odinger (NLS) equation. While earlier studies have examined such states in the realm of real…
We develop a class of soliton solution of {\it linear} Schr\"odinger equation without external potential. The quantum probability density generates its own boundary inside which there is internal vibration whose wave number is determined by…
The effective dynamics of solitons for the generalized nonlinear Schr\"odinger equation in a random potential is rigorously studied. It is shown that when the external potential varies slowly in space compared to the size of the soliton,…
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 wide class of localized and periodic…
We study the dynamics and pairwise interactions of dark soliton stripes in the two-dimensional defocusing nonlinear Schr\"odinger equation. By employing a variational approach we reduce the dynamics for dark soliton stripes to a set of…
We consider the interaction of a nonlinear Schrodinger soliton with a localized (point) defect in the medium through which it travels. Using numerical simulations, we find parameter regimes under which the soliton may be reflected,…
We theoretically investigate the scattering of bright solitons in a Bose-Einstein condensate on narrow attractive potential wells. Reflection, transmission and trapping of an incident soliton are predicted to occur with remarkably abrupt…
We investigate the soliton dynamics for a class of nonlinear Schr\"odinger equations with a non-local nonlinear term. In particular, we consider what we call {\em generalized Choquard equation} where the nonlinear term is $(|x|^{\theta-N} *…
We consider the 3-dimensional nonlinear Schr\"{o}dinger equation (NLS) with average nonlinearity. This is a limiting model of NLS with strong magnetic confinement and a generalized model of the resonant system of NLS with a partial harmonic…
The Cauchy problem of the modified nonlinear Schr\"{o}dinger (mNLS) equation with the finite density type initial data is investigated via $\overline{\partial}$ steepest descent method. In the soliton region of space-time $x/t\in(5,7)$, the…