Generalized traveling-wave solutions of nonlinear reaction–diffusion equations with delay and variable coefficientsстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 6 марта 2019 г.
Аннотация:The paper presents a number of new exact solutions to nonlinear reaction-diffusion equations with delay of the form
$$
c(x)u_t=[a(x)u_x]_x+b(x)F(u,w),\quad \ w=u(x,t-\tau),
$$
where $\tau>0$ is the delay time, and $f(u,w)$ is an arbitrary function of two arguments.
Solutions are sought in the form of a generalized traveling-wave, $u=U(z)$ with $z=t+\theta(x)$.
It is shown that one of the two functional coefficients $a(x)$ and $b(x)$ of the equation considered can be specified arbitrarily. Examples of delay reaction-diffusion equations and their solutions are given. New exact solutions of few other nonlinear delay PDEs are also obtained.