Symmetry operators of a Hartree-type equation with quadratic potential

Результат исследований: Материалы для журналаСтатья

1 Цитирования (Scopus)

Аннотация

We study the symmetry properties of a nonstationary one-dimensional Hartree-type equation with quadratic periodic potential and nonlocal nonlinearity. We find an explicit form of a nonlinear evolution operator for this equation and obtain a solution to a Cauchy problem in the class of semiclassically concentrated functions. We find parametric families of nonlinear symmetry operators of a Hartree-type equation (keeping invariant the set of solutions to this equation). Using the symmetry operators, we construct families of exact solutions to the equation. This approach constructively extends the ideas and methods of group analysis to the case of nonlinear integro-differential equations.

Язык оригиналаАнглийский
Страницы (с-по)119-132
Число страниц14
ЖурналSiberian Mathematical Journal
Том46
Номер выпуска1
DOI
СостояниеОпубликовано - 1 янв 2005

ASJC Scopus subject areas

  • Mathematics(all)

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