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We introduce a general model which augments the one-dimensional nonlinear Schr\"{o}dinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a…

An asymmetric pair of coupled nonlinear Schr{\"o}dinger (CNLS) equations has been derived through a multiscale perturbation method applied to a plasma fluid model, in which two wavepackets of distinct carrier wavenumbers and amplitudes are…

In the present paper an introduction to the new subject of nonlinear dispersive hamiltonian equations on graphs is given. The focus is on recently established properties of solutions in the case of nonlinear Schr\"odinger equation. Special…

We consider the one-dimensional propagation of electromagnetic waves in a weakly nonlinear and low-contrast spatially inhomogeneous medium with no energy dissipation. We focus on the case of a periodic medium, in which dispersion enters…

In this paper we develop a new approximation method valid for a wide family of nonlinear wave equations of Nonlinear Schr\"odinger type. The result is a reduced set of ordinary differential equations for a finite set of parameters measuring…

We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schr{\"o}dinger (NLS) equation. The method of studying the stability relies on freezing the radial…

In a recent work we studied the first nonlinear stage of modulation instability (NLSMI) of x-periodic anomalous (rogue, freak, extreme) waves (AWs) of physically relevant multidimensional (generalizations of the focusing) nonlinear…

In this paper we consider a family of time-dependent 1-dimensional cubic Schr\"odinger equation (NLS) with periodic potential. Exploiting semiclassical scaling and multiscale analysis, we derive an effective nonlinear Dirac equation, which…

In this work, we study the existence and orbital (in)stability of certain standing-wave solutions for the cubic nonlinear Schr\"odinger equation (NLS) posed on a looping-edge graph $\mathcal{G}$, consisting of a circle and a finite number…

A nonlinear extension of Schr\"odinger's wave equation is proposed that ensures non-signaling by keeping linear the evolution of \textit{coordinate-diagonal} elements of the density matrix. The equation contains a negative kinetic energy…

A nonlinear Schr\"odinger equation (NLS) with dispersion averaged nonlinearity of saturated type is considered. Such a nonlocal NLS is of integro-differential type and it arises naturally in modeling fiber-optics communication systems with…

The nonlinear Schr\"odinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains, albeit in differing amplitude-frequency domains. In this paper, we take advantage of the…

We demonstrate theoretically and numerically that the fundamental Raman soliton of the widely used nonlinear Schroedinger equation (NLSE) with a linear approximation of the Raman gain ({\em reduced} NLSE) is metastable. It can propagate for…

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…

The focusing Nonlinear Schr\"odinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, and MI is considered the main physical mechanism for the…

This paper completes the program started in arXiv:2104.11204 and arXiv:2110.04565 aiming at providing a full rigorous justification of the wave kinetic theory for the nonlinear Schr\"odinger (NLS) equation. Here, we cover the full range of…

The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the…

We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…

We consider the cubic nonlinear Schr\"odinger (NLS) equation with a linear damping on the one dimensional torus and we investigate the stability of some solitary wave profiles within the dissipative dynamics. The undamped cubic NLS equation…

We study a deformation of the defocusing nonlinear Schr\"odinger (NLS) equation, the defocusing Camassa- Holm NLS, hereafter referred to as CH-NLS equation. We use asymptotic multiscale expansion methods to reduce this model to a…