Related papers: Multi-parametric solutions to the NLS equation
We derive the two-breather solution of the class I infinitely extended nonlinear Schrodinger equation (NLSE). We present a general form of this multi-parameter solution that includes infinitely many free parameters of the equation and free…
A multidomain spectral method with compactified exterior domains combined with stable second and fourth order time integrators is presented for Schr\"odinger equations. The numerical approach allows high precision numerical studies of…
Recently, an integrable system of coupled (2+1)-dimensional nonlinear Schrodinger (NLS) equations was introduced by Fokas (eq. (18) in Nonlinearity 29}, 319324 (2016)). Following this pattern, two integrable equations [eqs.2 and 3] with…
We generalise a previously published approach based on a multi-domain spectral method on the whole real line in two ways: firstly, a fully explicit 4th order method for the time integration, based on a splitting scheme and an implicit…
The infinite families of Peregrine, Akhmediev and Kuznetsov-Ma breather solutions of the focusing Nonlinear Schroedinger (NLS) equation are obtained via a matrix version of the Darboux transformation, with a spectral matrix of the form of a…
We consider the nonlinear Schr\"odinger equation with non-local derivatives in a two-dimensional periodic domain. For certain orders of derivatives, we find a new type of breather solution dominating the field evolution at low nonlinearity…
In this paper we develop a bilinearisation-reduction approach to derive solutions to the classical and nonlocal nonlinear Schr\"{o}dinger (NLS) equations with nonzero backgrounds. We start from the second order Ablowitz-Kaup-Newell-Segur…
The data recorded in optical fiber [1] and in hydrodynamic [2] experiments reported the pioneering observation of nonlinear waves with spatiotemporal localization similar to the Peregrine soliton are examined by using nonlinear spectral…
We consider NLS on $\T^2$ with multiplicative spatial white noise and nonlinearity between cubic and quartic. We prove global existence, uniqueness and convergence almost surely of solutions to a family of properly regularized and…
We consider a nonlinear dispersive equation with a quasilinear quadratic term. We establish two results. First, we show that solutions to this equation with initial data of order $\mathcal{O}(\varepsilon)$ in Sobolev norms exist for a time…
The nonlinear Schr{\"o}odinger (NLS) equation, which incorporates higher-order dispersive terms, is widely employed in the theoretical analysis of various physical phenomena. In this study, we explore the non-commutative extension of the…
In this article, we show that the solution to defocusing cubic nonlinear Schr\"odinger equation (NLS) posed on the two-dimensional waveguide \begin{align*} i\partial_tu+\Delta_{\R\times\T}u=|u|^2u \end{align*} is globally well-posed in…
The Peregrine breather is widely discussed as a model for rogue waves in deep water. We present here a detailed numerical study of perturbations of the Peregrine breather as a solution to the nonlinear Schr\"odinger (NLS) equations. We…
We look for normalized solutions to the nonlinear Schr\"{o}dinger equation with mixed fractional Laplacians and combined nonlinearities $$ \left\{\begin{array}{ll} (-\Delta)^{s_{1}} u+(-\Delta)^{s_{2}} u=\lambda u+\mu |u|^{q-2}u+|u|^{p-2}u…
The nonlinear Schr\"{o}dinger (NLS) equation can be derived as a formal approximation equation describing the envelopes of slowly modulated spatially and temporarily oscillating wave packet-like solutions to the ion Euler-Poisson equation.…
In this paper, we present a microscopic derivation of the two-dimensional focusing cubic nonlinear Schr\"odinger equation starting from an interacting $N$-particle system of Bosons. The interaction potential we consider is given by…
We construct series solutions to all orders for breathers of Klein-Gordon equations, in powers of an amplitude parameter epsilon, under a sign condition on the coefficients of the expansion of the nonlinearity. All terms may be computed…
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, breather, dromion and lump solutions. These…
We consider reduced-order modeling of nonlinear dispersive waves described by a class of nonlinear Schrodinger (NLS) equations. We compare two nonlinear reduced-order modeling methods: (i) The reduced Lagrangian approach which relies on the…
We consider the one dimensional focusing (cubic) Nonlinear Schr\"odinger equation (NLS) in the semiclassical limit with exponentially decaying complex-valued initial data, whose phase is multiplied by a real parameter. We prove smooth…