Symmetry reductions and new functional separable solutions of nonlinear Klein–Gordon and telegraph type equationsстатья
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Дата последнего поиска статьи во внешних источниках: 4 марта 2020 г.
Аннотация:The paper is concerned with different classes of nonlinear Klein--Gordon and
telegraph type equations with variable coefficients
\begin{align*}
c(x)u_{tt}+d(x)u_t=[a(x)u_x]_x+b(x)u_x+p(x)f(u),
\end{align*}
where $f(u)$ \arbf. We seek exact solutions to these equations by the direct
method of symmetry reductions using the composition of functions $u=U(z)$
with $z=\varphi(x,t)$. We show that $f(u)$ and any four of the five
functional coefficients $a(x)$, $b(x)$, $c(x)$, $d(x)$, and $p(x)$ in such
equations can be set arbitrarily, while the remaining coefficient can be expressed in terms
of the others. The study investigates the properties and finds some solutions of the
overdetermined system of PDEs for $\varphi(x,t)$. Examples of
specific equations with new exact functional separable solutions are given.
In addition, the study presents some generalized traveling wave solutions to more
complex, nonlinear Klein--Gordon and telegraph type equations with delay.