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Approximate double-periodic solutions in \((1+1)\)-dimensional \(\varphi^4\)-theory. (English. Russian original) Zbl 0917.35115

Theor. Math. Phys. 116, No. 2, 881-889 (1998); translation from Teor. Mat. Fiz. 116, No. 2, 182-192 (1998).
Summary: Double-periodic solutions of the Euler-Lagrange equation for the \((1+1)\)-dimensional scalar \(\varphi^4\)-theory are considered. The nonlinear term is assumed to be small, and the Poincaré method is used to seek asymptotic solutions in the standing-wave form. The principal resonance problem, which arises for zero mass, is resolved if the leading-order term is taken in the form of a Jacobi elliptic function.

MSC:

35Q40 PDEs in connection with quantum mechanics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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