** O. A. Khrustalev**^{1}

*Institute for Theoretical Problems of Microphysics,
Moscow State University,
Department of Physics, Moscow State University,
Moscow, 119899, Russia *

and

Moscow, 119899, Russia

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Doubly periodic (periodic both in time
and in space) solutions for the Lagrange-Euler
equation of the (1+1)-dimensional scalar theory are studied. Provided that nonlinear term is small, the
Poincare-Lindstedt
asymptotic method is used to find asymptotic solutions in the standing
wave form. It is proved that using the
Jacobi elliptic function **cn ** as the zero approximation one can solve
the problem of the main resonance, appearing in the case of zero mass, and
construct a uniform expansion.

- Introduction
- Asymptotic solutions in the standing wave form
- The standing wave solutions for the massless theory
- Conclusions
- Bibliography
- About this document ...

IMACS ACA'98 Electronic Proceedings