Sobolev norms of $L^2$-solutions to NLS

Abstract

We apply inverse spectral theory to study Sobolev norms of solutions to the nonlinear Schrodinger equation. For initial datum $q_0\in L^2(\mathbb{R})$ and $s\in [-1,0]$, we prove that there exists a conserved quantity that is equivalent to $H^s(\mathbb{R})$-norm of the solution.

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Cited by in corpus (1)

• The conservative Camassa-Holm flow with step-like irregular initial data