INTEGRABILITY CONDITIONS FOR COMPLEX SYSTEMS WITH HOMOGENEOUS QUINTIC NONLINEARITIES

Brigita Ferčec; Xingwu Chen; Valery G. Romanovski

doi:10.11948/2011002

2011 Volume 1 Issue 1

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Brigita Ferčec, Xingwu Chen, Valery G. Romanovski. INTEGRABILITY CONDITIONS FOR COMPLEX SYSTEMS WITH HOMOGENEOUS QUINTIC NONLINEARITIES[J]. Journal of Applied Analysis & Computation, 2011, 1(1): 9-20. doi: 10.11948/2011002

Citation:

Brigita Ferčec, Xingwu Chen, Valery G. Romanovski. INTEGRABILITY CONDITIONS FOR COMPLEX SYSTEMS WITH HOMOGENEOUS QUINTIC NONLINEARITIES[J]. Journal of Applied Analysis & Computation, 2011, 1(1): 9-20. doi: 10.11948/2011002

INTEGRABILITY CONDITIONS FOR COMPLEX SYSTEMS WITH HOMOGENEOUS QUINTIC NONLINEARITIES

1 CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia;
2 CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia;
3 Faculty of Natural Science and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia

Abstract

Abstract

In this paper we obtain conditions for the existence of a local analytic flrst integral for four eight-parameter families of quintic complex system. We also discuss computational di-culties arising in the study of the problem of integrability for these systems.
- Integrability /
- center problem /
- time-reversibility /
- polynomial vector fleld /
- Darboux integral
MSC: 34C05;37C10

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References

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