Construction of doubly periodic solutions via the Poincare-Lindstedt method in the case of massless phi(4) theoryстатья
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Аннотация:Doubly periodic (periodic both in time and in space) solutions for the Lagrange-Euler equation of the (1 + 1)-dimensional scalar phi (4) theory are studied. Provided that the nonlinear term is small, the Poincare-Lindstedt asymptotic method can be used to find asymptotic solutions in the standing wave form. The principal resonance problem, which arises for zero mass, is solved if the leading-order term is taken in the form of Jacobi elliptic function. To obtain this leading-order term the system REDUCE is used. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.