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This work deals with soliton solutions of the nonlinear Schroedinger equation with cubic and quintic nonlinearities. We extend the procedure put forward in a recent Letter and we solve the equation in the presence of linear background, and…
We discuss the existence of breather solutions for a Discrete Nonlinear Schr\"odinger equation in an infinite $N$-dimensional lattice, involving site dependent anharmonic parameter. We give a simple proof on the existence of (nontrivial)…
In this paper we present soliton solutions of two coupled nonlinear Schodinger equations modulated in the bspace and time. The approach allows us to obatin solitons with large variety of solutions depending on the nonlinearity and the…
We find exact solutions to nonlinear Schr\"odinger equation in the presence of self-steepening and self-frequency shift. These include periodic solutions and localized solutions of dark-bright type which can be {\emph{chiral}}, and…
We look for solutions to derivative nonlinear Schrodinger equations built upon solitons. We prove the existence of multi-solitons i.e. solutions behaving at large time as the sum of finite solitons. We also show that one can attach a kink…
We present a one-line closed form expression for the three-parameter breather of the nonlinear Schr\"odinger equation. This provides an analytic proof of the time period doubling observed in experiments. The experimental check that some…
We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…
The existence of breather type solutions, i.e., periodic in time, exponentially localized in space solutions, is a very unusual feature for continuum, nonlinear wave type equations. Following an earlier work [Comm. Math. Phys. {\bf 302},…
We consider the cubic defocusing nonlinear Schr\"odinger equation in one dimension with the nonlinearity concentrated at a single point. We prove global well-posedness in the scaling-critical space $L^2(\mathbb{R})$ and scattering for all…
In this paper, we study the Cauchy problem of the nonlinear Schr\"{o}dinger equation with a nontrival potential $V_\varepsilon(x)$. In particular, we consider the case where the initial data is close to a superposition of $k$ solitons with…
A numerical study of the nonlinear Schr\"odinger (NLS) equation subject to homogeneous Dirichlet, Neumann and Robin boundary conditions in the finite line is presented. The results are compared with both the exact analytical ones for the…
We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the…
In this paper we announce the result of asymptotic dynamics of solitons of nonlinear Schrodinger equations with external potentials. To each local minima of the potential there is a soliton centered around it. Under some conditions on the…
The long-time asymptotic behavior of solutions to the focusing nonlinear Schr\"odinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity is studied in the case of initial conditions that allow for the…
We present a simple approach for finding $N$-soliton solution and the corresponding Jost solutions of the derivative nonlinear Scr\"{o}dinger equation with nonvanishing boundary conditions. Soliton perturbation theory based on the inverse…
We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of…
In this paper, an extended nonlinear Schrodinger equation with higher-order that includes fifth-order dispersion with matching higher-order nonlinear terms is investigated under zero boundary condition at infinity. Carrying out the spectral…
In this paper, we introduce the reverse-space and reverse-space-time nonlocal discrete derivative nonlinear Schr\"odinger (DNLS) equations through the nonlocal symmetry reductions of the semi-discrete Gerdjikov-Ivanov equation. The…
We study soliton solutions of a modified non-linear Schroedinger (MNLS) equation. Using an Ansatz for the time and azimuthal angle dependence previously considered in the studies of the spinning Q-balls, we construct multi-node solutions of…
We consider the 3D cubic nonlinear Schr\"odinger equation (NLS) with a strong toroidal trap. In the first part, we show that as the confinement is strengthened, a large class of global solutions to the time-dependent model can be described…