Construction of doubly periodic solutions via the Poincare–Lindstedt method in the case of massless ϕ4 theory

Doubly periodic (periodic both in time and in space) solutions for the Lagrange–Euler equation of the (1+1)-dimensional scalar ϕ4 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.