Nonlinear Dynamics

, Volume 63, Issue 1–2, pp 205–215 | Cite as

The monotonicity and critical periods of periodic waves of the φ 6 field model

  • Aiyong Chen
  • Jibin Li
  • Wentao Huang
Original Paper


In this paper, we study the relationship between period and energy of periodic traveling wave solutions for the φ 6 field model. The various topological phase portraits with periodic annulus are given by using standard phase portrait analytical technique. Some analytic behaviors (convexity, monotonicity and number of critical periods) of the period functions associated with periodic waves are investigated. We prove that the period function has exactly one critical period under certain conditions. Moreover, the numerical simulation is made. The results show that our theoretical analysis agrees with the numerical simulation.


Period function Critical period Periodic wave φ6 field model 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Center of Nonlinear Science StudiesKunming University of Science and TechnologyKunmingP.R. China
  2. 2.School of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilinP.R. China

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