Тип публикации: статья из журнала
Год издания: 2009
Идентификатор DOI: 10.1134/S0081543809030134
Аннотация: Darboux's classical results about transformations of second-order hyperbolic equations by means of differential substitutions are extended to the case of parabolic equations of the form Lu = (D (x) (2) + a(x, y)D (x) + b(x, y)D (y) + c(x, y))u = 0. We prove a general theorem that provides a way to determine admissible differential Показать полностьюsubstitutions for such parabolic equations. It turns out that higher order transforming operators can always be represented as a composition of first-order operators that define a series of consecutive transformations. The existence of inverse transformations imposes some differential constrains on the coefficients of the initial operator. We show that these constraints may imply famous integrable equations, in particular, the Boussinesq equation.
Журнал: PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
Выпуск журнала: Vol. 266, Is. 1
Номера страниц: 219-227
ISSN журнала: 00815438
Место издания: NEW YORK
Издатель: MAIK NAUKA/INTERPERIODICA/SPRINGER