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math.SP2014
Hill's Spectral Curves and the Invariant Measure of the Periodic KdV Equation
Gordon Blower, Caroline Brett, Ian Doust
This paper analyses the periodic spectrum of Schrödinger's equation when the potential is real, periodic, random and subject to the invariant measure of the pe…
math.SP2013
Logarithmic Sobolev inequalities and spectral concentration for the cubic Schrödinger equation
Gordon Blower, Caroline Brett, Ian Doust
The nonlinear Schrödinger equation NLSE(p, β), -iu_t=-u_{xx}+β| u|^{p-2} u=0, arises from a Hamiltonian on infinite-dimensional phase space \Lp^2(\mT). For p\leq 6, Bourgain (Comm.…