Related papers: Talbot Effect for the Manakov System on the Torus
We study the evolution of the one dimensional periodic cubic Schr\"odinger equation (NLS) with bounded variation data. For the linear evolution, it is known that for irrational times the solution is a continuous, nowhere differentiable…
In this paper, we investigate the dichotomous behavior of solutions to the Kawahara equation with bounded variation initial data, analogous to the Talbot effect. Specifically, we observe that the solution is quantized at rational times,…
We study Dirichlet-type problems for the simplest third-order linear dispersive PDE, often referred to as the Airy equation. Such problems have not been extensively studied, perhaps due to the complexity of the spectral structure of the…
We demonstrate the fractional Talbot effect of nonpraxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutions of the Helmholtz equation in two dimensions. The effect…
The Talbot effect describes the emergence of periodic patterns in perturbed propagating wave fields. The effect is well studied for perturbations from structurally coherent optics such as diffraction gratings. The emergence of freeform and…
A frequency comb generated from a phase-modulated continuous-wave laser is simultaneously subject to the temporal Talbot effect and modulational instability (MI) when propagating through a piece of optical fiber. The temporal Talbot effect…
The Manakov system is a two-component nonlinear Schr\"odinger equation. The long-time asymptotics for the defocusing or focusing Manakov system under nonzero background still remains open. In this paper, we derive the long-time asymptotic…
Under periodic boundary conditions, a one-dimensional dispersive medium driven by a Lamb oscillator exhibits a smooth response when the dispersion relation is asymptotically linear or superlinear at large wave numbers, but unusual fractal…
The temporal Talbot effect refers to the periodic self-imaging of pulse trains in optical fibers. The connection between the linear and nonlinear temporal Talbot effect is still not fully understood. To address this challenge, we use…
In this paper, the dispersive revival and fractalization phenomena for bidirectional dispersive equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles are investigated. Firstly, we study…
We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D…
The temporal Talbot effect refers to the periodic revivals of a pulse train propagating in a dispersive medium, and is a temporal analog of the spatial Talbot effect with group-velocity dispersion in time replacing diffraction in space.…
We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the perturbed nonlinear Schrodinger (NLS) equation and the Manakov model. The perturbations include the simultaneous by a periodic external…
We consider linear, time-dependent and skew-adjoint perturbations of periodic transport equations on the one-dimensional torus. We describe the long-time behavior of solutions for all non-degenerate perturbations in resonant regime, proving…
In spite of the massive interest that the generalized Manakov equation has attracted in the past two decades, no physical system which is quantitatively described by this equation has been reported so far. In this paper we show that…
Aim of the paper is to provide a method to analyze the behavior of $T$-periodic solutions $x_\eps, \eps>0$, of a perturbed planar Hamiltonian system near a cycle $x_0$, of smallest period $T$, of the unperturbed system. The perturbation is…
We study the long time behavior of the stochastic quantization equation. Extending recent results by Mourrat and Weber we first establish a strong non-linear dissipative bound that gives control of moments of solutions at all positive times…
A new two-component system with cubic nonlinearity and linear dispersion: \begin{eqnarray*} \left\{\begin{array}{l} m_t=bu_{x}+\frac{1}{2}[m(uv-u_xv_x)]_x-\frac{1}{2}m(uv_x-u_xv), \\ n_t=bv_{x}+\frac{1}{2}[ n(uv-u_xv_x)]_x+\frac{1}{2}…
We prove the well-posedness of the Cauchy problem on torus to an eletromagnetoelastic system. The physical model consists of three coupled partial differential equations, one of them is a hyperbolic equation describing the elastic medium…
We investigate, both analytically and numerically, dispersive fractalization and quantization of solutions to periodic linear and nonlinear Fermi-Pasta-Ulam-Tsingou systems. When subject to periodic boundary conditions and discontinuous…