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用近似Lie对称性理论研究弱非线性耦合二维各向异性 谐振子的一阶近似Lie对称性与近似守恒量, 并以频率比为2:1的弱非线性耦合二维各向异性谐振子为例, 得到其6个一阶近似Lie对称性和一阶近似守恒量, 其中1个一阶近似守恒量实为系统的精确守恒量, 4个一阶近似守恒量为平凡的一阶近似守恒量, 只有1 个一阶近似守恒量为稳定的一阶近似守恒量.
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关键词:
- 弱非线性耦合二维各向异性谐振子 /
- 近似Lie对称性 /
- 近似守恒量
The first-order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator are studied. When the 1/2 is equal to 2/1, the system possesses six first-order approximate Lie symmetries and approximate conserved quantities, one of them is an exact conserved quantity, four of them are trivial conserved quantities, only one of them is a stable conserved quantity.-
Keywords:
- weak nonlinear coupled two-dimensional anisotropic harmonic oscillator /
- approximate Lie symmetries /
- approximate conserved quantity
[1] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) p90 (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用 (北京: 科学出版社) 第90页]
[2] Zhao Y Y, Mei F X 1999 Symmetries and Invariants of Mechanical System (Beijing: Science Press) p1 (in Chinese) [赵跃宇, 梅凤翔 1999 力学系统的对称性与不变量 (北京: 科学出版社)第1页]
[3] Lou Z M 2007 Chin. Phys. 16 1182
[4] Fu J L, Chen L Q, Chen X W 2006 Chin. Phys. 15 8
[5] Jia L Q, Xie J F, Luo S K 2008 Chin. Phys. B 17 1560
[6] Lou Z M 2007 Acta Phys. Sin. 56 2475 (in Chinese) [楼智美 2007 56 2475]
[7] Fang J H 2010 Chin. Phys. B 19 040301
[8] Zhang Y 2011 Chin. Phys. B 20 034502
[9] Leach P G L, Moyo S, Cotsakis S, Lemmer R L 2001 J. Nonlinear Math. Phys. 8 139
[10] Govinder K S, Heil T G, Uzer T 1998 Phys. Lett. A 240 127
[11] Kara A H, Mahomed F M, Unal G 1999 Int. J. Theoret. Phys. 38 2389
[12] Unal G 2000 Phys. Lett. A 269 13
[13] Unal G 2001 Nonlinear Dyn. 26 309
[14] Unal G, Gorali G 2002 Nonlinear Dyn. 28 195
[15] Feroze T, Kara A H 2002 Int. J. Non-linear Mech. 37 275
[16] Ibragimov N H, Unal G, Jogreus C 2004 J. Math. Anal. Appl. 297 152
[17] Dolapci I T, Pakdemirli M 2004 Int. J. Non-linear Mech. 39 1603
[18] Kara A H, Mahomed F M, Qadir A 2008 Nonlinear Dyn. 51 183
[19] Pakdemirli M, Yurusoy M, Dolapci I T 2004 Acta Appl. Math. 80 243
[20] Johnpillai A G, Kara A H, Mahomed F M 2006 Int. J. Non-linear Mech. 41 830
[21] Grebenev V N, Oberlack M 2007 J. Nonlinear Math. Phys. 14 157
[22] Johnpillai A G, Kara A H, Mahomed F M 2009 J. Comput. Appl. Math. 223 508
[23] Lou Z M 2010 Acta Phys. Sin. 59 6764 (in Chinese) [楼智美 2010 59 6764]
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[1] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) p90 (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用 (北京: 科学出版社) 第90页]
[2] Zhao Y Y, Mei F X 1999 Symmetries and Invariants of Mechanical System (Beijing: Science Press) p1 (in Chinese) [赵跃宇, 梅凤翔 1999 力学系统的对称性与不变量 (北京: 科学出版社)第1页]
[3] Lou Z M 2007 Chin. Phys. 16 1182
[4] Fu J L, Chen L Q, Chen X W 2006 Chin. Phys. 15 8
[5] Jia L Q, Xie J F, Luo S K 2008 Chin. Phys. B 17 1560
[6] Lou Z M 2007 Acta Phys. Sin. 56 2475 (in Chinese) [楼智美 2007 56 2475]
[7] Fang J H 2010 Chin. Phys. B 19 040301
[8] Zhang Y 2011 Chin. Phys. B 20 034502
[9] Leach P G L, Moyo S, Cotsakis S, Lemmer R L 2001 J. Nonlinear Math. Phys. 8 139
[10] Govinder K S, Heil T G, Uzer T 1998 Phys. Lett. A 240 127
[11] Kara A H, Mahomed F M, Unal G 1999 Int. J. Theoret. Phys. 38 2389
[12] Unal G 2000 Phys. Lett. A 269 13
[13] Unal G 2001 Nonlinear Dyn. 26 309
[14] Unal G, Gorali G 2002 Nonlinear Dyn. 28 195
[15] Feroze T, Kara A H 2002 Int. J. Non-linear Mech. 37 275
[16] Ibragimov N H, Unal G, Jogreus C 2004 J. Math. Anal. Appl. 297 152
[17] Dolapci I T, Pakdemirli M 2004 Int. J. Non-linear Mech. 39 1603
[18] Kara A H, Mahomed F M, Qadir A 2008 Nonlinear Dyn. 51 183
[19] Pakdemirli M, Yurusoy M, Dolapci I T 2004 Acta Appl. Math. 80 243
[20] Johnpillai A G, Kara A H, Mahomed F M 2006 Int. J. Non-linear Mech. 41 830
[21] Grebenev V N, Oberlack M 2007 J. Nonlinear Math. Phys. 14 157
[22] Johnpillai A G, Kara A H, Mahomed F M 2009 J. Comput. Appl. Math. 223 508
[23] Lou Z M 2010 Acta Phys. Sin. 59 6764 (in Chinese) [楼智美 2010 59 6764]
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