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Coupled terms are present in the Lagrangian and the corresponding differential equations of a two-dimensional charged oscillator system are nonlinearly coupled. Firstly, the coupled terms in the Lagrangian are eliminated by transformation of coordinates; secondly, the conserved quantities in new coordinates are obtained by direct integral method, and the approximate solutions are obtained by Abdomina decomposition method. Finally, the conserved quantities and the approximate solutions can be expressed in original coordinates by using the inverse transform of the coordinates. The discussion of the approximate solutions is also given in this paper.
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Keywords:
- two-dimensional charged coupled oscillator system /
- conserved quantities /
- approximate sloutions
[1] Lou Z M 2013 Acta Phys. Sin. 62 220201 (in Chinese)[楼智美 2013 62 220201]
[2] Lou Z M, Mei F X 2012 Acta Phys. Sin. 61 110201 (in Chinese)[楼智美, 梅凤翔 2012 61 110201]
[3] Ding G T 2013 Acta Phys. Sin. 62 064502
[4] Ding G T 2013 Acta Phys. Sin. 62 064501
[5] Mei F X 2003 Acta Phys. Sin. 52 1048 (in Chinese)[梅凤翔 2003 52 1048]
[6] Zhang Y 2012 Acta Phys. Sin. 61 214501 (in Chinese)[张毅 2012 61 214501]
[7] Lou Z M 2007 Chin. Phys. 16 1182
[8] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[9] Cui J C, Han Y L, Jia L Q 2012 Chin. Phys. B 21 080201
[10] Zhao L, Fu J L, Chen B Y 2011 Chin. Phys. B 20 040201
[11] Nucci M C 2011 Phys. Lett. A 375 1375
[12] Choudhuri A, Ghosh S, Talukdar B 2008 J. Phys. 70 657
[13] Lutzky M 1998 Int. J. Non-Linear Mech. 33 393
[14] Fang J Q, Yao W G 1993 Acta Phys. Sin. 42 1375 (in Chinese)[方锦清, 姚伟光 1993 42 1375]
[15] Fang J Q 1993 Progress in Phys. 13 441 (in Chinese) [方锦清 1993 物理学进展 13 441]
[16] Hosseini M M 2006 J. Comput. l Appl. Math. 197 495
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[1] Lou Z M 2013 Acta Phys. Sin. 62 220201 (in Chinese)[楼智美 2013 62 220201]
[2] Lou Z M, Mei F X 2012 Acta Phys. Sin. 61 110201 (in Chinese)[楼智美, 梅凤翔 2012 61 110201]
[3] Ding G T 2013 Acta Phys. Sin. 62 064502
[4] Ding G T 2013 Acta Phys. Sin. 62 064501
[5] Mei F X 2003 Acta Phys. Sin. 52 1048 (in Chinese)[梅凤翔 2003 52 1048]
[6] Zhang Y 2012 Acta Phys. Sin. 61 214501 (in Chinese)[张毅 2012 61 214501]
[7] Lou Z M 2007 Chin. Phys. 16 1182
[8] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[9] Cui J C, Han Y L, Jia L Q 2012 Chin. Phys. B 21 080201
[10] Zhao L, Fu J L, Chen B Y 2011 Chin. Phys. B 20 040201
[11] Nucci M C 2011 Phys. Lett. A 375 1375
[12] Choudhuri A, Ghosh S, Talukdar B 2008 J. Phys. 70 657
[13] Lutzky M 1998 Int. J. Non-Linear Mech. 33 393
[14] Fang J Q, Yao W G 1993 Acta Phys. Sin. 42 1375 (in Chinese)[方锦清, 姚伟光 1993 42 1375]
[15] Fang J Q 1993 Progress in Phys. 13 441 (in Chinese) [方锦清 1993 物理学进展 13 441]
[16] Hosseini M M 2006 J. Comput. l Appl. Math. 197 495
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