Optical-fluid dark line and X solitary waves in Kerr media

Abstract

Abstract:We consider the existence and propagation of nondi ractive and nondispersive spatiotemporal optical wavepackets in nonlinear Kerr media. We report analytically and con rm numerically the properties of spatiotemporal dark line solitary wave solutions of the ( + )D nonlinear Schrödinger equation (NLSE). Dark lines represent holes of light on a continuous wave background. Moreover, we consider nontrivial web patterns generated under interactions of dark line solitary waves, which give birth to dark X solitary waves. These solitary waves are derived by exploiting the connection between the NLSE and a wellknown equation of hydrodynamics, namely the ( + )D type II Kadomtsev-Petviashvili (KP-II) equation. This nding opens a novel path for the excitation and control of optical solitary waves, of hydrodynamic nature.

Stationary Solutions for Nonlinear Schrödinger Equations by Lie Group Analysis

“…The governing NLSE shows up in distinctive fields, including fluid dynamics, nonlinear optics and plasma physics. A lot of work has been done to find soliton solutions for various forms of NLSEs [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Eslami and Neirameh studied the exact soliton solutions for higher order NLSE [13].…”

Flux singularities in multiphase wavetrains and the Kadomtsev‐Petviashvili equation with applications to stratified hydrodynamics

“…The elements of the vector multiplying the third-order dispersive term are defined as = −⟨⟨̂, (̂) 4 ⟩⟩,…”

“…The equation itself models waves for which dispersion balances nonlinear steepening effects and weak transverse effects, and is a generalization of the one spatial dimension Korteweg‐de Vries (KdV) equation. First arising within the context of plasma physics, it has since been recognized to be a universal equation in the sense that it arises across a variety of different applications such as water waves, nonlinear optics, and Bose‐Einstein condensates …”

“…RATLIFF Korteweg-de Vries (KdV) equation. First arising within the context of plasma physics, 1 it has since been recognized to be a universal equation in the sense that it arises across a variety of different applications such as water waves, 2,3 nonlinear optics, 4,5 and Bose-Einstein condensates. 6,7 The principal aim of this paper is to illustrate how the KP equation (1) arises naturally from a phase dynamical perspective utilizing solutions parameterized by multiple phase variables, such as wavetrains.…”

Phase Dynamics of the Dysthe Equation and the Bifurcation of Plane Waves

“…In the study of this paper, we will utilise the various nonlinear dispersive reductions and illustrate how these structures can be interpreted as a deformation under the perturbation of the wave variables by the solitary wave solutions of these systems. This is not a novel idea, and is a technique utilised in other works [3,9,26,23]. Depending on the phase dynamical description, which itself depends on the properties of the moving frame, we will illustrate that a wealth of various structures are predicted to form from this viewpoint.…”