一类一维陈列的弧波特征

Abstract

Abstract:

Travelling wave solution in a one dimensional array of two degre of freedom Hamiltonian system is considered. We show that in the long wave limit, the problem can be reduced to the analysis of the honoclinic orbits of perturbed system. with a resonance in the unperturbed system, we show that the perturbed system have multi pulse honoclinic orbits asgmptotic to a periodic orbit, or fixed points using energy phase method.Therefore,the array have travelling wave solutions analogous to multi pulse solitons.

Key words: 　ａｒｒａｙ, ｅｎｅｒｇｙｐｈａｓｅｍｅｔｈｏｄ, ｍｕｌｔｉｐｕｌｓｅｈｏｍｏｃｌｉｎｉｃ, ｓｏｌｉｔｏｎ．

CLC Number:

３４Ｃ３５，３４Ｄ１０

Chen Liping. Character as solitary wave in a certain one-dimensional array[J].Acta mathematica scientia,Series A, 1999, 19(4): 361-367.

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References

１　ＳｔｒｏｇａｔｚＳＨ，ＭｉｒｏｌｌｏＲＺ．ＳｐｌａｙｓｔａｔｅｓｉｎｇｌｏｂａｌｌｙｃｏｕｐｌｅｄＪｏｓｅｐｈｓｏｎａｒｒａｙｓ：ＡｎａｌｙｔｉｃａｌｐｒｅｄｉｃｔｉｏｎｏｎＦｌｏｑｕｅｔｍｕｌｔｉｐｌｉｅｒｓ．ＰｈｙｓＲｅｖＥ，１９９３，４７：２２０～２２７
２　ＫｕｒａｍｏｔｏＹ．ＣｈｅｍｉｃａｌＯｓｃｉｌｌａｔｏｒｓ，ｗａｖｅｓａｎｄＴｕｒｂｕｌｅｎｖｅ．ＮｅｗＹｏｒｋ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９８４
３　ＷｉｎｆｒｅｅＡＴ．ＴｈｅＧｅｏｍｅｔｒｙｏｆＢｉｏｌｏｇｉａｌＴｉｍｅ．Ｂｅｒｌｉｎ：Ｓｐｒｉｎｇｅｒ１９９０
４　ＤｅｆｏｎｔａｉｎｅｓＡＤ，ＰｏｍｅａｎＹ，ＲｏｓｔａｎｄＢ．Ｃｈａｉｎｏｆｃｏｕｐｌｅｄｂｉｓｔａｓｂｅｏｓｃｉｌｌａｔｏｒｓ：Ａｍｏｄｅｌ．ＰｈｙｓｉｃａＤ，１９９０，４６：２０１～２１６
５　ＲｕｌｋｏｖＮＦ，ＶｏｌｋｏｖｓｈｉｉＡＲ，ＲｏｄｒｉｇｕｅｚｌｏｚａｎｏＡ，ＤｅｌＲｉｏＺ，ＶｅｌａｒｄｅＭＧ．Ｓｙｎｃｈｒｏｎｏｕｓｃｈａｏｔｉｃｂｅｈａｖｉｏｒｏｆａｒｅｓｐｏｎｓｅｏｓｃｉｌｌａｔｏｒｗｉｔｈｃｈａｏｔｉｃｄｒｉｖｉｎｇ．Ｃｈａｏｓ，Ｓｏｌｉｔｏｎｓ＆Ｆｒａｃｔａｌ，１９９４，４（１）：２０１～２１１
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７　ＨａｌｌｅｒＧ，ＷｉｇｇｉｎｓＳ．ＭｕｌｔｉＰｕｌｓｅｊｕｍｐｉｎｇｏｒｂｉｔｓａｎｄｈｏｍｏｃｔｉｎｉｃｔｒｅｅｓｉｎａｍｏｄａｌｔｒｕｎｃａｔｉｏｎｏｆｔｈｅｄａｍｐｅｄｆｏｒｃｅｄｎｏｎｌｉｎｅａｒＳｃｈｒ¨ ｏｄｉｎｇｅｒｅｑｕａｔｉｏｎ，ＰｈｙｓｉｃａＤ，１９９５，８５：３１１～３４７
８　ＨａｌｌｅｒＧ，ＷｉｇｇｉｎｓＳ．ＧｅｏｍｅｔｒｙａｎｄＣｈａｏｓｎｅａｒｒｅｓｏｎａｎｔｅｑｕｉｌｉｂｒｉｕｍｏｆ３ＤＯＦＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓ，ＰｈｙｓｉｃａＤ，１９９６，９０：３１９～３６５
９　ＨａｌｌｅｒＧ，ＷｉｇｇｉｎｓＳ．ＮｐｕｌｓｅｈｏｍｏｃｌｉｎｉｃｏｒｂｉｔｓｉｎｐｅｒｔｕｒｂａｔｉｏｎｓｏｆｒｅｓｏｎａｎｔＨａｍｉｌｔｏｎｉａｎＳｙｓｔｅｍｓ．ＡｒｃｈＲａｔＭｅｃｈＡｎａｌ，１９９５，１３０：２５
１０　ＨａｌｌｅｒＧ，ＷｉｇｇｉｎｓＳ．Ｏｒｂｉｔｓｈｏｍｏｃｌｉｎｉｃｔｏｒｅｓｏｎａｎｃｅｓ：ｔｈｅＨａｍｉｌｔｏｎｉａｎｃａｓｅ．ｐｈｙｓｉａＤ，１９９３，６６：２９８～３４６
１１　ＦｅｎｉｃｈｅｌＮ．Ｐｅｒｓｉｓｔｅｎｃｅａｎｄｓｍｏｔｈｎｅｓｓｏｆｉｖａｒｉａｎｔｍａｎｉｆｏｌｄｓｆｏｒｆｌｏｗｓ．ＩｎｄＵｎｉｖＭａｔｈＪ，１９７１，２１：１９３
１２　郭柏灵，庞小峰．孤立子．北京：科学出版社，１９８７
１３　刘适达，刘适式．孤波和湍流．上海：上海科技教育出版社，１９９４

[1]	CHEN Ping-Yan, GUAN Zong-Ping. Strong Law for Moving Average Processes of Arrays [J]. Acta mathematica scientia,Series A, 2010, 30(6): 1394-1401.
[2]	Pang Shanqi; Zhang Yingshan. Multiplication of Orthogonal Arrays [J]. Acta mathematica scientia,Series A, 2007, 27(3): 568-576.
[3]	QIU De-Hua, GAN Shi-Shen. Convergence of Arrays of rho Mixing Random Variables [J]. Acta mathematica scientia,Series A, 2005, 25(1): 73-78.

Character as solitary wave in a certain one-dimensional array

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