Related papers: Forced Nonlinear Schroedinger Equation with Arbitr…
We derive a class of discrete nonlinear Schr{\"o}dinger (DNLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic problem. It is demonstrated that the derived class of…
In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal…
Effects of nonlinear dynamics of solitary waves and wave modulations within the modular (also known as quadratically cubic) Korteweg - de Vries equation are studied analytically and numerically. Large wave events can occur in the course of…
In this paper, we study the existence and instability of standing waves with a prescribed $L^2$-norm for the fractional Schr\"{o}dinger equation \begin{equation} i\partial_{t}\psi=(-\Delta)^{s}\psi-f(\psi), \qquad (0.1)\end{equation} where…
We study the existence and stability of standing waves solutions of a three-coupled nonlinear Schr\"{o}dinger system related to the Raman amplification in a plasma. By means of the concentration-compacteness method, we provide a…
The nonlinear Schr\"odinger equation (NLSE) models the slowly varying envelope dynamics of a weakly nonlinear quasi-monochromatic wave packet in dispersive media. In the context of Bose-Einstein condensate (BEC), it is often referred to as…
We obtain exact solutions of the nonlinear Dirac equation in 1+1 dimension of the form $\Psi(x,t) = \Phi(x) e^{-i \omega t}$ where the nonlinear interactions are a combination of vector-vector (V-V) and scalar-scalar (S-S) interactions with…
The damped driven nonlinear Schr\"odinger equation (NLSE) has been used to understand a range of physical phenomena in diverse systems. Studying this equation in the context of optical hyper-parametric oscillators in anomalous-dispersion…
For the one dimensional nonlinear Schr\"odinger equation with triple power nonlinearity and general exponents, we study analytically and numerically the existence and stability of standing waves. Special attention is paid to the curves of…
We prove a sufficient condition for nonlinear stability of relative equilibria in the planar $N$-vortex problem. This result builds on our previous work on the Hamiltonian formulation of its relative dynamics as a Lie--Poisson system. The…
We introduce spatiotemporal optical dark X solitary waves of the (2+1)D {hyperbolic} nonlinear Schr\"odinger equation (NLSE), that rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are…
We study a nonlinear Schr\"odinger equation with logarithmic nonlinearity on a star graph $\mathcal{G}$. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\alpha\in \mathbb{R}$. We…
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…
The long-time asymptotics is analyzed for finite energy solutions of the 1D discrete Schr\"odinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group. For initial states…
We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…
We numerically investigate the long time dynamics of spatially periodic breather solutions of the 1-D nonlinear Schr\"odinger equation under parametric forcing of the form $f(x)=f_0 \exp(iKx)$ along with dissipation. In the absence of…
Dynamics of solitons is considered in the framework of an extended nonlinear Schrodinger equation (NLSE), which is derived from a system of the Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves. The…
We demonstrate that stabilization of solitons of the multidimensional Schrodinger equation with a cubic nonlinearity may be achieved by a suitable periodic control of the nonlinear term. The effect of this control is to stabilize the…
We revisit aspects of dynamics and stability of localized states in the deterministic and stochastic discrete nonlinear Schr\"odinger equation. By a combination of analytic and numerical techniques, we show that localized initial conditions…
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…