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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