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Teoreticheskaya i Matematicheskaya Fizika, 1977, Volume 31, Number 1, Pages 23–32
(Mi tmf2850)
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This article is cited in 3 scientific papers (total in 4 papers)
Solutions of “double soliton” type for the multidimensional equation $\Box u=F(u)$
V. S. Buslaev
Abstract:
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.
Received: 08.07.1976
Citation:
V. S. Buslaev, “Solutions of “double soliton” type for the multidimensional equation $\Box u=F(u)$”, TMF, 31:1 (1977), 23–32; Theoret. and Math. Phys., 31:1 (1977), 293–299
Linking options:
https://www.mathnet.ru/eng/tmf2850 https://www.mathnet.ru/eng/tmf/v31/i1/p23
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Abstract page: | 301 | Full-text PDF : | 95 | References: | 46 | First page: | 3 |
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