Solutions of “double soliton” type for the multidimensional equation $\Box u=F(u)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 31 (1977) no. 1, pp. 23-32
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Let $V$ be an even function, the Taylor series of which takes the form $V(u)\sim\frac{u^2}{2!}-\frac{u^4}{4!} + au^6 + \dots$ . It is shown that there exists the unique nontrivial series $u=\sum\limits_{k\geq 0} u_k (\xi,\eta)\mu^{2k}$, $\xi=\mu x$, $\eta=\omega^{-1}\mu\cos \omega t$, $\mu=\sqrt{1-\omega^2}$ ($\omega, \omega^2<1$ – is arbitrary parameter), which satisfies the equation $\Box u=-V'(u)$ and the coefficients of which are exponentially decreasing functions.
@article{TMF_1977_31_1_a2,
author = {V. S. Buslaev},
title = {Solutions of {\textquotedblleft}double soliton{\textquotedblright} type for the multidimensional equation $\Box u=F(u)$},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {23--32},
year = {1977},
volume = {31},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1977_31_1_a2/}
}
V. S. Buslaev. Solutions of “double soliton” type for the multidimensional equation $\Box u=F(u)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 31 (1977) no. 1, pp. 23-32. http://geodesic.mathdoc.fr/item/TMF_1977_31_1_a2/
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