New exact solutions of nonlinear wave type PDEs with delayстатья
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: 7 июля 2020 г.
Аннотация:We consider nonlinear wave type PDEs with delay of the form $$u_{tt}+H_1(u)u_t=[G(u)u_x]_x+H_2(u)u_x+F(u,w),$$ where $u=u(x,t)$ is the unknown function, $w=u(x,t-\tau)$, and $\tau$ is the delay time.The source function $F(u,w)$ depends on one or several arbitrary functions of one argument.Using the modified method of functional constraints,we obtain a number of new exact solutions with generalized and functional separation of variables, as well as traveling-wave solutions. Most solutions areexpressed in terms of elementary functions and contain free parameters. These solutions can be used to formulate test problems intended to evaluate theaccuracy of numerical methods for solving nonlinear delay PDEs.