INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA

doi:10.1007/s10473-020-0102-3

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (1): 16-34.doi: 10.1007/s10473-020-0102-3

INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA

王春花¹, 周静^1,2

1. School of Mathematics and Statistics and Hubei Key Laboratory Mathematical Sciences, Central China Normal University, Wuhan 430079, China;
2. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430000, China

收稿日期:2018-11-27 修回日期:2019-05-10 出版日期:2020-02-25 发布日期:2020-04-14
通讯作者: Jing Zhou E-mail:zhouj@mail.scuec.edu.cn
基金资助:
This paper was partially supported by NSFC (11671162; 11601194), CCNU18CXTD04 and CZQ13017.

INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA

Chunhua WANG¹, Jing ZHOU^1,2

1. School of Mathematics and Statistics and Hubei Key Laboratory Mathematical Sciences, Central China Normal University, Wuhan 430079, China;
2. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430000, China

Received:2018-11-27 Revised:2019-05-10 Online:2020-02-25 Published:2020-04-14
Contact: Jing Zhou E-mail:zhouj@mail.scuec.edu.cn
Supported by:
This paper was partially supported by NSFC (11671162; 11601194), CCNU18CXTD04 and CZQ13017.

摘要/Abstract

摘要：

In this paper, we consider the following coupled Schr?dinger system with χ⁽²⁾ nonlinearities

which arises from second-harmonic generation in quadratic media. Here V₁(x) and V₂(x) are radially positive functions, 2 ≤ N < 6, α > 0 and α > β. Assume that the potential functions V₁(x) and V2(x) satisfy some algebraic decay at infinity. Applying the finite dimensional reduction method, we construct an unbounded sequence of non-radial vector solutions of synchronized type.

关键词: χ⁽²⁾ nonlinearities, second-harmonic generation, synchronized solution, reduction method

Abstract:

In this paper, we consider the following coupled Schr?dinger system with χ⁽²⁾ nonlinearities

Key words: χ⁽²⁾ nonlinearities, second-harmonic generation, synchronized solution, reduction method

中图分类号:

35J10

王春花, 周静. INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA[J]. 数学物理学报(英文版), 2020, 40(1): 16-34.

Chunhua WANG, Jing ZHOU. INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA[J]. Acta mathematica scientia,Series B, 2020, 40(1): 16-34.

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INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA

INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA

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