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Abstract: We present numerical simulations of the defocusing nonlinear SchrodingerNLS equation with an energy supercritical nonlinearity. These computationswere motivated by recent works of Kenig-Merle and Kilip-Visan who consideredsome energy supercritical wave equations and proved that if the solution is {apriori} bounded in the critical Sobolev space i.e. the space whose homogeneousnorm is invariant under the scaling leaving the equation invariant, then itexists for all time and scatters.In this paper, we numerically investigate the boundedness of the$H^2$-critical Sobolev norm for solutions of the NLS equation in dimension fivewith quintic nonlinearity.We find that for a class of initial conditions, this norm remains bounded,the solution exists for long time, and scatters.



Author: J. Colliander, G. Simpson, C. Sulem

Source: https://arxiv.org/







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