Search results for "wave equation"
showing 10 items of 74 documents
Modeling of photonic crystal fibers from the scalar wave equation with a purely transverse linearly polarized vector potential
2011
In this work, we propose a new technique for modeling light propagation in photonic crystal fibers where the electric field is evaluated from a purely transverse linearly polarized vector potential. The vector potential in a nonuniform dielectric obeys a wave equation coupled to the scalar potential, but it can be reduced to a scalar wave equation when the coupling term is ignored to the lowest order approximation. We show that this method gives reliable results for photonic crystal fibers when the scalar analysis is improved by a perturbational correction.
Dark- and bright-rogue-wave solutions for media with long-wave–short-wave resonance
2014
5 pags.; 5 figs.; PACS number(s): 46.40.−f, 47.20.Ky, 47.35.−i, 47.52.+j
The fixed angle scattering problem with a first order perturbation
2021
We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by $2n$ measurements up to a natural gauge. We also show that one can recover the full first order term for a related equation having no gauge invariance, and that it is possible to reduce the number of measurements if the coefficients have certain symmetries. This work extends the fixed angle scattering results of Rakesh and M. Salo to Hamiltonians with first order perturbations, and it is based on wave equation methods and Carleman estimates.
Digital rock physics: Effect of fluid viscosity on effective elastic properties
2011
Abstract This paper is concerned with the effect of pore fluid viscosity on effective elastic properties using digitized rocks. We determine a significant velocity dispersion in wave propagation simulations by the variation of the pore fluid viscosity. Several attenuation regimes are considered which may contribute to this observation. Starting point is a virtual rock physics approach. Numerical simulations of effective transport and effective mechanical properties are applied to statistically representative rock samples. The rock microstructure is imaged by 3D X-ray tomography. Permeability values were estimated through Lattice-Boltzmann flow simulations. The dry rock moduli and the tortuo…
Large Time Behavior for Inhomogeneous Damped Wave Equations with Nonlinear Memory
2020
We investigate the large time behavior for the inhomogeneous damped wave equation with nonlinear memory ϕtt(t,&omega
Scale-free relaxation of a wave packet in a quantum well with power-law tails
2013
We propose a setup for which a power-law decay is predicted to be observable for generic and realistic conditions. The system we study is very simple: A quantum wave packet initially prepared in a potential well with (i) tails asymptotically decaying like ~ x^{-2} and (ii) an eigenvalues spectrum that shows a continuous part attached to the ground or equilibrium state. We analytically derive the asymptotic decay law from the spectral properties for generic, confined initial states. Our findings are supported by realistic numerical simulations for state-of-the-art expansion experiments with cold atoms.
Scattering on Riemannian Symmetric Spaces and Huygens Principle
2018
International audience; The famous paper by L. D. Faddeev and B. S. Pavlov (1972) on automorphic wave equation explored a highly romantic link between Scattering Theory (in the sense of Lax and Phillips) and Riemann hypothesis. An attempt to generalize this approach to general semisimple Lie groups leads to an interesting evolution system with multidimensional time explored by the author in 1976. In the present paper, we compare this system with a simpler one defined for zero curvature symmetric spaces and show that the Huygens principle for this system in the curved space holds if and only if it holds in the zero curvature limit.
Multi-rogue waves solutions to the focusing NLS equation and the KP-I equation
2011
Abstract. We construct a multi-parametric family of quasi-rational solutions to the focusing NLS equation, presenting a profile of multiple rogue waves. These solutions have also been used by us to construct a large family of smooth, real localized rational solutions of the KP-I equation quite different from the multi-lumps solutions first constructed in Bordag et al. (1977). The physical relevance of both equations is very large. From the point of view of geosciences,the focusing NLS equation is relevant to the description of surface waves in deep water, and the KP-I equation occurs in the description of capillary gravitational waves on a liquid surface, but also when one considers magneto…
The nonlinear Schrodinger equation and the propagation of weakly nonlinear waves in optical fibres and on the water surface
2015
International audience; The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional par…
Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser
2004
The multiple-period pulsations of the soliton parameters in a passively mode-locked fiber laser were discussed numerically and experimentally. It was found that the pulse acquired a periodic evolution that was not related to the round-trip time and consisted of many round trips. The macroperiodicity existed independently or in combination with other periodicity such as period doubling, tripling etc. Analysis shows that the new periods in the soliton modulation appear at bifurcation point related to certain points related to certain values of the cavity parameters.