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A real weak nonlinear coupled two-dimensional system is constructed first by using coupling spring with variable force constant. The first-order approximate Lie symmetries and approximate conserved quantities of the system are studied. The system possesses six first-order approximate Lie symmetries and approximate conserved quantities, of which one is an exact conserved quantity, four are trivial conserved quantities, and only one is a stable conserved quantity.
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Keywords:
- weak nonlinear coupled two-dimensional system /
- 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) p103, p303 (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103页, 第303页]
[2] Dong W S, Wang B X, Fang J H 2011 Chin. Phys. B 20 010204
[3] Chen R, Xu X J 2012 Chin. Phys. B 21 094510
[4] Fang J H 2010 Chin. Phys. B 19 040301
[5] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[6] Xie Y L, Jia L Q, Luo S K 2011 Chin. Phys. B 20 010203
[7] Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 60 060201]
[8] Han Y L, Sun X T, Zhang Y Y, Jia L Q 2013 Acta Phys. Sin. 62 160201 (in Chinese)[韩月林, 孙现亭, 张耀宇, 贾利群 2013 62 160201]
[9] Leach P G L, Moyo S, Cotsakis S, Lemmer R L 2001 J. Nonlinear Math. Phys. 1 139
[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]
[24] Lou Z M, Mei F X, Chen Z D 2012 Acta Phys. Sin. 61 110204 (in Chinese) [楼智美, 梅凤翔, 陈子栋 2012 61 110204]
[25] Zhang Z Y, Yong X L, Chen Y F 2009 Chin. Phys. B 19 2629
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[1] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems(Beijing: Science Press) p103, p303 (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103页, 第303页]
[2] Dong W S, Wang B X, Fang J H 2011 Chin. Phys. B 20 010204
[3] Chen R, Xu X J 2012 Chin. Phys. B 21 094510
[4] Fang J H 2010 Chin. Phys. B 19 040301
[5] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[6] Xie Y L, Jia L Q, Luo S K 2011 Chin. Phys. B 20 010203
[7] Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 60 060201]
[8] Han Y L, Sun X T, Zhang Y Y, Jia L Q 2013 Acta Phys. Sin. 62 160201 (in Chinese)[韩月林, 孙现亭, 张耀宇, 贾利群 2013 62 160201]
[9] Leach P G L, Moyo S, Cotsakis S, Lemmer R L 2001 J. Nonlinear Math. Phys. 1 139
[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]
[24] Lou Z M, Mei F X, Chen Z D 2012 Acta Phys. Sin. 61 110204 (in Chinese) [楼智美, 梅凤翔, 陈子栋 2012 61 110204]
[25] Zhang Z Y, Yong X L, Chen Y F 2009 Chin. Phys. B 19 2629
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