caa a22 4500 445361085 CHVBK 20180317142915.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s11071-010-9797-0 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9797-0 The monotonicity and critical periods of periodic wavesofthe φ 6 field model [Elektronische Daten] [Aiyong Chen, Jibin Li, Wentao Huang] 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. Springer Science+Business Media B.V., 2010 Period function nationallicence Critical period nationallicence Periodic wave nationallicence φ 6 field model nationallicence Chen Aiyong Center of Nonlinear Science Studies, Kunming University of Science and Technology, 650093, Kunming, Yunnan, P.R. China aut Li Jibin Center of Nonlinear Science Studies, Kunming University of Science and Technology, 650093, Kunming, Yunnan, P.R. China aut Huang Wentao School of Mathematics and Computing Science, Guilin University of Electronic Technology, 541004, Guilin, Guangxi, P.R. China aut Nonlinear Dynamics Springer Netherlands 63/1-2(2011-01-01), 205-215 0924-090X 63:1-2<205 2011 63 11071 https://doi.org/10.1007/s11071-010-9797-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9797-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chen Aiyong Center of Nonlinear Science Studies, Kunming University of Science and Technology, 650093, Kunming, Yunnan, P.R. China aut NATIONALLICENCE 700 1- Li Jibin Center of Nonlinear Science Studies, Kunming University of Science and Technology, 650093, Kunming, Yunnan, P.R. China aut NATIONALLICENCE 700 1- Huang Wentao School of Mathematics and Computing Science, Guilin University of Electronic Technology, 541004, Guilin, Guangxi, P.R. China aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 63/1-2(2011-01-01), 205-215 0924-090X 63:1-2<205 2011 63 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer