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

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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 $u=\sum\limits_{k\geq 0} u_k (\xi,\eta)\mu^{2k}$, $\xi=\mu x$, $\eta=\omega^{-1}\mu\cos \omega t$, $\mu=\sqrt{1-\omega^2}$ ($\omega, \omega^21$ – 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 ``double soliton'' 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},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1977_31_1_a2/}
}
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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/