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

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【作者】 王春花； 周静；

【Author】 Chunhua WANG;Jing ZHOU;School of Mathematics and Statistics and Hubei Key Laboratory Mathematical Sciences,Central China Normal University;School of Mathematics and Statistics, South-Central University for Nationalities;

【通讯作者】 周静;

【机构】 School of Mathematics and Statistics and Hubei Key Laboratory Mathematical Sciences,Central China Normal University； School of Mathematics and Statistics, South-Central University for Nationalities；

【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.

【Abstract】 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；
【Key words】 χ（2）nonlinearities； second-harmonic generation； synchronized solution； reduction method；
【基金】 partially supported by NSFC(11671162; 11601194);CCNU18CXTD04 and CZQ13017
  • 【文献出处】 Acta Mathematica Scientia ,数学物理学报(英文版) , 编辑部邮箱 ,2020年01期
  • 【分类号】O411
  • 【被引频次】1
  • 【下载频次】17
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