Construction of Special Solutions for Nonintegrable Systems

DOI

10.2991/jnmp.2006.13.1.5How to use a DOI?

Abstract

The Painlev´e test is very useful to construct not only the Laurent series solutions of systems of nonlinear ordinary differential equations but also the elliptic and trigonmetric ones. The standard methods for constructing the elliptic solutions consist of two independent steps: transformation of a nonlinear polynomial differential equation into a nonlinear algebraic system and a search for solutions of the obtained system. It has been demonstrated by the example of the generalized H´enon­Heiles system that the use of the Laurent series solutions of the initial differential equation assists to solve the obtained algebraic system. This procedure has been automatized and generalized on some type of multivalued solutions. To find solutions of the initial differential eqution in the form of the Laurent or Puiseux series we use the Painlev´e test. This test can also assist to solve the inverse problem: to find the form of a polynomial potential, which corresponds to the required type of solutions. We consider the five­dimensional gravitational model with a scalar field to demonstrate this.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Sergey Yu. Vernov
PY  - 2006
DA  - 2006/02/01
TI  - Construction of Special Solutions for Nonintegrable Systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 50
EP  - 63
VL  - 13
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2006.13.1.5
DO  - 10.2991/jnmp.2006.13.1.5
ID  - Vernov2006
ER  -