IKBFU's Vestnik

2015 Issue №04

Back to the list Download an article

The Abel equation and cosmological scalar field zeroes



This article presents a new simple analytical method that makes it possi-ble to design solutions in describing the dynamics of the universe near the ze-roes of the scalar field potential.


1. Yurov V. А. An application of Abel’s equation of first kind to the search of solutions of Friedman’s equations // Вестник РГУ им. И. Канта. 2010. Т. 4. С. 43—47.
2. Yurov A. V., Yurov V. A. Friedman vs. Abel: A connection unraveled // Journal of Mathematical Physics. 2010. Vol. 51. P. 082503: 1—17.
3. Yurov A. V., Yaparova A. V., Yurov V. A. Application of Abel Equation of 1st kind to in ation analysis for non-exactly solvable cosmological models // European Physical Journal. 2014. Vol. 20, Iss. 2. P. 106—115.
4. Muslimov A. G. On The Scalar Field Dynamics In A Spatially Flat Friedman Universe // Class. Quant. Grav. 1990. Vol. 7. P. 231—237.
5. Salopek D. S., Bond J. R. Nonlinear evolution of long-wavelength metric  fluctuations in inflationary models // Phys. Rev. D. 1990. Vol. 42. P. 3936—3962.
6. Bazeia D., Santos M. J. dos, Ribeiro R. F. Solitons in systems of coupled scalar fields // Phys. Lett. A. 1995. Vol. 208. P. 84—88.
7. Aref'eva I.Ya., Koshelev A. S., Vernov S.Yu. Crossing the w = – 1 barrier in the D3-brane dark energy model // Phys. Rev. D. 2005. Vol. 72. P. 064017: 1—11.
8. Yurov A. V., Yurov V. A., Chervon S. V., Sami M. Total energy potential as a su-perpotential in integrable cosmological models // Theoretical and Mathematical Physics. 2011. Vol. 166, Iss. 2. P. 299—311.
9. Chervon S. V., Zhuravlev V. M., Shcigolev V. K. New Exact Solutions in Standart Inflationary Models // Phys. Lett. B. 1997. Vol. 395. P. 269—273.