Geodesic
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 
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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     title = {Solutions of {\textquotedblleft}double soliton{\textquotedblright} type for the multidimensional equation $\Box u=F(u)$},
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     volume = {31},
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     language = {ru},
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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.

[1] N. A. Voronov, I. Yu. Kobzarev, N. B. Konyukhova, Pisma v ZhETF, 22 (1975), 590

[2] R. Finkelshtein, R. Le-Leve, M. Ruderman, Nelineinaya kvantovaya teoriya polya, Sb., IL, 1959

[3] L. A. Takhtadzhyan, L. D. Faddeev, UMN, 29:3 (1974), 249 | MR

[4] R. F. Dashen, B. Hasslacher, A. Heveu, Phys. Rev., D11 (1975), 3424 | MR