Semiclassically Concentrates Waves for the Nonlinear Schrödinger Equation with External Field
نویسندگان
چکیده
Classes of solutions, asymptotic in small parameter , → 0, are constructed to the generalized nonlinear Schrödinger equation (NSE) in a multi-dimensional space with an external field in the framework of the WKB-Maslov method. Asymptotic semiclassically concentrated solutions (SCS), regarded as multi-dimensional solitary waves, are introduced for the NSE with an external field and cubic local nonlinearity. The one-dimensional soliton dynamics in an external field of a special form is discussed. Another class of asymptoitic SCS solutions is constructed for the NSE with Gaussian non-local potential and a local external field. These solutions are similar to the trajectory-coherent states or squeezed states in quantum mechanics.
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