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Teoreticheskaya i Matematicheskaya Fizika, 1984, Volume 59, Number 3, Pages 440–452
(Mi tmf5029)
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This article is cited in 2 scientific papers (total in 2 papers)
Integration of the $\varphi^4$ model in elliptic Jacobi functions and investigation of them by the phase plane method
V. E. Grishin, V. K. Fedyanin
Abstract:
Solutions are obtained for the $\varphi^4$ model for different relationships between the signs
of the constants in the Hamiltonian in the form of Jacobi elliptic functions. Such
essentially nonlinear solutions, investigated on the phase plane, go over into kinks
or solitons in the limiting ease for the parameter E on the separatrices S. For the
lowest state $E_{\min}=U(\varphi_0)$ (vacuum), the solutions are transformed into a vacuum
condensate (harmonic oscillations). Expansion of the solutions near the vacuum
corresponds to the result of perturbation theory.
Received: 10.08.1983
Citation:
V. E. Grishin, V. K. Fedyanin, “Integration of the $\varphi^4$ model in elliptic Jacobi functions and investigation of them by the phase plane method”, TMF, 59:3 (1984), 440–452; Theoret. and Math. Phys., 59:3 (1984), 609–617
Linking options:
https://www.mathnet.ru/eng/tmf5029 https://www.mathnet.ru/eng/tmf/v59/i3/p440
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Abstract page: | 248 | Full-text PDF : | 88 | References: | 42 | First page: | 1 |
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