The trajectory-coherent approximation and the system of moments for the hartree type equation

Результат исследований: Материалы для журналаСтатьярецензирование

29 Цитирования (Scopus)

Аннотация

The general construction of semiclassically concentrated solutions to the Hartree type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter □ (□→0), are constructed with a power accuracy of O (□ N/2), where N is any natural number. In constructing the semiclassically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for centered moments) is essentially used. The nonlinear superposition principle has been formulated for the class of semiclassically concentrated solutions of Hartree type equations. The results obtained are exemplified by a one-dimensional Hartree type equation with a Gaussian potential.

Язык оригиналаАнглийский
Страницы (с-по)325-370
Число страниц46
ЖурналInternational Journal of Mathematics and Mathematical Sciences
Том32
Номер выпуска6
DOI
СостояниеОпубликовано - 1 янв 2002

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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