# Asymptotic behavior of the Schrödinger–Debye system with refractive index of quadratic wave amplitude

@article{Corcho2017AsymptoticBO,
title={Asymptotic behavior of the Schr{\"o}dinger–Debye system with refractive index of quadratic wave amplitude},
author={Ad{\'a}n J. Corcho and Juan C. Cordero},
journal={Letters in Mathematical Physics},
year={2017},
volume={108},
pages={2031-2054}
}
• Published 2 May 2017
• Mathematics
• Letters in Mathematical Physics
We obtain local well-posedness for the one-dimensional Schrödinger–Debye interactions in nonlinear optics in the spaces $$L^2\times L^p,\; 1\le p < \infty$$L2×Lp,1≤p<∞. When $$p=1$$p=1 we show that the local solutions extend globally. In the focusing regime, we consider a family of solutions $$\{(u_{\tau }, v_{\tau })\}_{\tau >0}$${(uτ,vτ)}τ>0 in $$H^1\times H^1$$H1×H1 associated to an initial data family $$\{(u_{\tau _0},v_{\tau _0})\}_{\tau >0}$${(uτ0,vτ0)}τ>0 uniformly bounded in H^1…

## References

SHOWING 1-9 OF 9 REFERENCES

• Mathematics
• 2011
We establish local well-posedness results for the Initial Value Problem associated to the Schr\"odinger-Debye system in dimensions $N=2, 3$ for data in $H^s\times H^{\ell}$, with $s$ and $\ell$
• Mathematics
• 2011
We establish local well-posedness results in weak periodic function spaces for the Cauchy problem of the Benney system. The Sobolev space $H^{1/2}\times L^2$ is the lowest regularity attained and
We study the Cauchy problem for two systems of equations (Maxwell-Debye and Maxwell-Bloch) describing laser-matter interaction phenomena. We show that these problems are locally in time well-posed
In this paper we study the local-in-time Cauchy problem for the Schrodinger–Debye equations. This model occurs in nonlinear optics and describes the non-resonant delayed interaction of an
• Mathematics
• 2009
1. The Fourier Transform.- 2. Interpolation of Operators.- 3. Sobolev Spaces and Pseudo-Differential Operators.- 4. The Linear Schrodinger Equation.- 5. The Non-Linear Schrodinger Equation.- 6.
• Physics
Applied optics
• 1966
In this method, non-linear susceptibility tensors are introduced which relate the induced dipole moment to a power series expansion in field strengths and the various experimental observations are described and interpreted in terms of this formalism.
• Mathematics
• 2001
The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in
Preliminaries The linear Schrodinger equation The Cauchy problem in a general domain The local Cauchy problem Regularity and the smoothing effect Global existence and finite-time blowup Asymptotic