KAM TORI FOR DEFOCUSING KDV-MKDV EQUATION

doi:10.1007/s10473-019-0119-4

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 243-258.doi: 10.1007/s10473-019-0119-4

KAM TORI FOR DEFOCUSING KDV-MKDV EQUATION

崔文艳, 弭鲁芳, 尹枥

College of Science, Binzhou University, Binzhou 256600, China

收稿日期:2017-04-06 修回日期:2018-10-15 出版日期:2019-02-25 发布日期:2019-03-13
通讯作者: Wenyan CUI E-mail:yufengxingshi@163.com
作者简介:Lufang MI,milufang@126.com;Li YIN,yinli_79@163.com
基金资助:
Supported by NSFC (11601036, 11401041), Science and Technology Foundation of Shandong Province (J16LI52).

KAM TORI FOR DEFOCUSING KDV-MKDV EQUATION

Wenyan CUI, Lufang MI, Li YIN

College of Science, Binzhou University, Binzhou 256600, China

Received:2017-04-06 Revised:2018-10-15 Online:2019-02-25 Published:2019-03-13
Contact: Wenyan CUI E-mail:yufengxingshi@163.com
Supported by:
Supported by NSFC (11601036, 11401041), Science and Technology Foundation of Shandong Province (J16LI52).

摘要/Abstract

摘要： In this paper, we consider small perturbations of the KdV-mKdV equation
u_t=-u_xxx + 6uu_x + 6u²u_x
on the real line with periodic boundary conditions. It is shown that the above equation admits a Cantor family of small amplitude quasi-periodic solutions under such perturbations. The proof is based on an abstract infinite dimensional KAM theorem.

关键词: quasi-periodic solution, KdV-mKdV equation, KAM theory, normal form

Abstract: In this paper, we consider small perturbations of the KdV-mKdV equation
u_t=-u_xxx + 6uu_x + 6u²u_x
on the real line with periodic boundary conditions. It is shown that the above equation admits a Cantor family of small amplitude quasi-periodic solutions under such perturbations. The proof is based on an abstract infinite dimensional KAM theorem.

Key words: quasi-periodic solution, KdV-mKdV equation, KAM theory, normal form

崔文艳, 弭鲁芳, 尹枥. KAM TORI FOR DEFOCUSING KDV-MKDV EQUATION[J]. 数学物理学报(英文版), 2019, 39(1): 243-258.

Wenyan CUI, Lufang MI, Li YIN. KAM TORI FOR DEFOCUSING KDV-MKDV EQUATION[J]. Acta mathematica scientia,Series B, 2019, 39(1): 243-258.

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KAM TORI FOR DEFOCUSING KDV-MKDV EQUATION

KAM TORI FOR DEFOCUSING KDV-MKDV EQUATION

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