This article is cited in 1 paper

Approximate double-periodic solutions in $(1+1)$-dimensional $\varphi ^4$-theory

S. Yu. Vernov^a, O. A. Khrustalev<sup>b

a</sup> Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University
^b M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: 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 Poincarй 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.

Received: 27.02.1998

DOI: 10.4213/tmf896

 English version: Theoretical and Mathematical Physics, 1998, 116:2, 881–889

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