New generalized and functional separable solutions to non-linear delay reaction-diffusion equationsстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 4 января 2018 г.
Аннотация:We present a number of new generalized separable, functional separable, periodic and antiperiodic exact solutions to non-linear delay reaction-diffusion equations of the form u(t) = ku(xx) + F(u,w), where u = u(x, t) and w = u(x, t-tau), with tau being the delay time. The generalized separable solutions are sought in the form u = Sigma(N)(n = 1) Phi(n)(x)Psi(n)(t), with the functions Phi(n)(x) and Psi(n)(t) to be determined in the analysis. Most of the equations considered contain one or two arbitrary functions of a single argument or one arbitrary function of two arguments of special form. All solutions involve free parameters (in some cases, infinitely many parameters) and so can be suitable for solving certain problems and testing approximate analytical and numerical methods for non-linear delay PDEs. Some results are extended to non-linear delay partial differential equations of any order.