相关论文: Higher dimensional localized and periodic wave dyn…
In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional KP-I equation and spin-nonlinear Schr\"odinger (spin-NLS) equation via the deep neural networks leaning. Moreover, the inverse…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
This thesis deals with some theoretical aspects of deterministic freak wave generation in the wave basin of a hydrodynamic laboratory. We adopt the spatial nonlinear Schr\"odinger equation as a mathematical model to describe the deformation…
In this work, modulation of periodic interfacial waves on a conduit of viscous liquid is explored utilizing Whitham theory and Nonlinear Schr\"odinger (NLS) theory. Large amplitude periodic wave modulation theory does not require…
The coupled-mode theory is developed for description of the nonlinear wave dynamics in binary optical lattices. The obtained equations of motion accurately describe nonlinear wave dynamics close to the band edges and in the gap of the…
The Hirota equation is a higher order extension of the nonlinear Schroedinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
Assume a lower-dimensional solitonic structure embedded in a higher dimensional space, e.g., a 1D dark soliton embedded in 2D space, a ring dark soliton in 2D space, a spherical shell soliton in 3D space etc. By extending the Landau…
A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak…
In this letter we introduce the concept of stabilized vector solitons as nonlinear waves constructed by addition of mutually incoherent Townes solitons that are stabilized under the effect of a periodic modulation of the nonlinearity. We…
This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which…
We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value problem. We propose a Fourier pseudo-spectral discretization of…
We describe a nonlinear kagome lattice with nonlinear dynamics described by Klein-Gordon interactions with a scalar unknown at each node, such as might occur in a nonlinear electrical lattice. We show that the dispersion relation has three…
The existence of stable solitons in two- and three-dimensional (2D and 3D) media governed by the self-focusing cubic nonlinear Schr\"{o}dinger equation with a periodic potential is demonstrated by means of the variational approximation (VA)…
We study nonlinear waves on a plane-wave background in an erbium-doped fiber system, which is governed by the coupled nonlinear Schr\"odinger and the Maxwell-Bloch equations. We find that prolific different types of nonlinear localized and…
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 study the propagation of femtosecond light pulses inside an optical fiber medium exhibiting higher-order dispersion and cubic-quintic nonlinearities. Pulse evolution in such system is governed by a higher-order nonlinear Schr%…
The phenomenon of dynamical localization of matter wave solitons in optical lattices is first demonstrated and the conditions for its existence are discussed. In addition to the trapping linear periodic potential we use a periodic…
We analyze two-component spatial optical vortex solitons supported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localised waves, namely, parametric vortex solitons due to phase-matched…
We study the dynamics of two-dimensional coherent structures in planetary atmospheres and oceans. We derive the Zakharov-Kuznetsov equation for large scale motion from the barotropic quasigeostrophic equation in a weakly nonlinear, long…