Higher dimensional solitary waves generated by second-harmonic generation in quadratic media

被引：33
|
作者：
Zhao, Leiga [1 ]
Zhao, Fukun [2 ]
Shi, Junping [3 ]
机构：
[1] Beijing Univ Chem Technol, Dept Math, Beijing 100029, Peoples R China
[2] Yunnan Normal Univ, Dept Math, Kunming 650092, Peoples R China
[3] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 54卷 / 03期
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
NONLINEAR SCHRODINGER-EQUATIONS; MULTIPLE BOUND-STATES; POSITIVE SOLUTIONS; ELLIPTIC-SYSTEMS; GROUND-STATE; EXISTENCE; BIFURCATION; UNIQUENESS; SOLITONS;
D O I：
10.1007/s00526-015-0879-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Schrodinger type soliton waves generated by second-harmonic generation in higher dimensional quadratic optical media are considered. The existence of ground state solutions for spatial dimension from two to five is proved, and the continuous dependence on the parameter and asymptotic behavior of ground state solutions are established. Multi-pulse solutions with certain symmetry are also obtained. In a bounded domain setting, global bifurcation diagram of multi-pulse solutions are shown by using new technique of double saddle-node bifurcation.
引用
收藏
页码：2657 / 2691
页数：35
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