878 research outputs found
Construction of Doubly Periodic Solutions via the Poincare-Lindstedt Method in the case of Massless Phi^4 Theory
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
considered. The nonlinear term is assumed to be small, and the
Poincare-Lindstedt method is 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 a Jacobi elliptic
function. It have been proved that the choice of elliptic cosine with fixed
value of module k (k=0.451075598811) as the leading-order term puts the
principal resonance to zero and allows us constructed (with accuracy to third
order of small parameter) the asymptotic solution in the standing wave form. To
obtain this leading-order term the computer algebra system REDUCE have been
used. We have appended the REDUCE program to this paper.Comment: 16 pages, LaTeX 2.09. This paper have been published in the
Electronic Proceedings of the Fourth International IMACS Conference on
Applications of Computer Algebra (ACA'98) {Prague (Czech Republic)} at
http://math.unm.edu/ACA/1998/sessions/dynamical/verno
Calculation of Heat-Kernel Coefficients and Usage of Computer Algebra
The calculation of heat-kernel coefficients with the classical DeWitt
algorithm has been discussed. We present the explicit form of the coefficients
up to in the general case and up to for the minimal parts.
The results are compared with the expressions in other papers. A method to
optimize the usage of memory for working with large expressions on universal
computer algebra systems has been proposed.Comment: 12 pages, LaTeX, no figures. Extended version of contribution to
AIHENP'95, Pisa, April 3-8, 199
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