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Mathematical and computational methods for semiclassical Schrödinger equations
(Cambridge University Press, 2011-05)
We consider time-dependent (linear and nonlinear) Schr¨odinger equations in a semiclassical scaling. These equations form a canonical class of (nonlinear) dispersive models whose solutions exhibit high-frequency oscillations. ...
Existence of solitary waves in dipolar quantum gases
We study a nonlinear Schrodinger equation arising in the mean eld description of dipolar quantum gases. Under the assumption of su- ciently strong dipolar interactions, the existence of standing waves, and hence solitons, ...