# 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} }

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…

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