Semiclassical Trajectory-Coherent Approximations of Hartree-Type Equations |
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Authors: | Belov V V Trifanov A Yu Shapovalov A V |
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Institution: | (1) Moscow Institute for Electronics and Mathematics, Moscow, Russia;(2) Tomsk Polytechnical University, Tomsk, Russia;(3) Tomsk State University, Tomsk, Russia |
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Abstract: | We use the concept of the complex WKB–Maslov method to construct semiclassically concentrated solutions for Hartree-type equations. Formal solutions of the Cauchy problem for this equation that are asymptotic (with respect to a small parameter , 0) are constructed with the power-law accuracy O(N/2), where N3 is a positive integer. The system of Hamilton–Ehrenfest equations (for averaged and centered moments) derived in this paper plays a significant role in constructing semiclassically concentrated solutions. In the class of semiclassically concentrated solutions of Hartree-type equations, we construct an approximate Green's function and state a nonlinear superposition principle. |
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