Geodesic
Approximate double-periodic solutions in $(1+1)$-dimensional $\varphi ^4$-theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 2, pp. 182-192

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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. 
@article{TMF_1998_116_2_a1,
     author = {S. Yu. Vernov and O. A. Khrustalev},
     title = {Approximate double-periodic solutions in $(1+1)$-dimensional $\varphi ^4$-theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {182--192},
     publisher = {mathdoc},
     volume = {116},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_116_2_a1/}
}
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S. Yu. Vernov; O. A. Khrustalev. Approximate double-periodic solutions in $(1+1)$-dimensional $\varphi ^4$-theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 2, pp. 182-192. http://geodesic.mathdoc.fr/item/TMF_1998_116_2_a1/