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Using the generalized variational iteration method, a class of nonlinear disturbed evolution equations are studied. Firstly, a functional is introduced, then its variational is computed, and the iteration expansion is finally constructed. The approximate and exact analytic solutions to the problem are obtained.
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Keywords:
- evolution equation /
- perturbation /
- variational iteration
[1] McPhaden M J, Zhang D 2002 Nature 415 603
[2] Gu D F, Philander S G H 1994 Science 275 805.
[3] Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 10 (in Chinese) [刘式适、傅遵涛、刘式达、赵 强 2002 51 10]
[4] Pan L X, Zuo W M, Yan J R 1995 Acta Phys. Sin. 54 1 (in Chinese) [潘留仙、左伟明、颜家壬 2002 54 1]
[5] Pan L X, Liu J L, Li S S, Niu Z C, Feng S L, Zheng H Z 2002 Sci. Chin. 32A 556 (in Chinese) [潘留仙、刘金龙、李树深、牛智川、封松林、郑厚植 2002 中国科学 32A 556]
[6] Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林、董文杰、贾晓静、曹鸿兴 2002 51 1181]
[7] Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林、戴新刚、王爱慧、丑纪范 2001 50 606]
[8] Lin W T, Ji Z Z, Wang B, Zhang X 2002 Prog. Nat. Sci. 12 1326
[9] Wang L S, Xu D Y 2003 Sci. Chin. 32E 488 (in Chinese) [王林山、徐道义 2003 中国科学 32E 488]
[10] Mo J Q, Lin W T 2008 J. Sys. Sci. Complexity 20 119
[11] Mo J Q, Wang H 2007 Acta Ecologica Sin. 27 4366
[12] Mo J Q 2009 Chin. Phys. Lett. 26 060202
[13] Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese) [莫嘉琪 2009 58 2930]
[14] Mo J Q, Cheng Y 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、程 燕 2009 58 4379]
[15] Mo J Q 2009 Acta Phys. Sin.2009 58 695 (in Chinese) [莫嘉琪 2009 58 695]
[16] Mo J Q, Yao J S 2008 Acta Phys. Sin. 2008 57 7419 (in Chinese) [莫嘉琪、姚静荪 2008 57 7419]
[17] Mo J Q 2009 Sci. Chin. 52G 1007
[18] Mo J Q, Lin W T, Wang H 2007 Chin. Phys. 16 578
[19] Mo J Q, Lin W T, Wang H 2007 Prog. Nat. Sci. 17 230
[20] Mo J Q, Lin W T, Wang H 2008 Chin. Geographical Sci. 18 193
[21] Mo J Q, Lin W T 2008 Chin. Phys. 17 370
[22] Mo J Q, Lin W T 2008 Chin. Phys. 17 743
[23] Mo J Q 2010 Chin. Phys. 19 010203
[24] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. 19 030202
[25] Huang N N 1996 Theory of Solitons and Method of Perturbations (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [黄念宁 1996 孤子理论和扰动方法(上海:上海科技教育出版社)]
[26] Pan L X, Yan J R, Zhou G H 2001 Chin. Phys. 10 594
[27] Zheng Q, Yue P 2006 Chin. Phys. 15 35
[28] He H S, Chen J, Yang K Q 2005 Chin. Phys. 14 1926
[29] Lu F L, Chen C Y 2005 Chin. Phys. 14 463
[30] Zhang X A, Chen K, Duan Z I 2005 Chin. Phys. 14 42
[31] Teman R 1988 Infinite-Dimensional Dynamical System in Mechnica and Physica (New York: Springer)
[32] Zhu Z W, Lu Y 2000 J. Xhin. Quart. Math. 15 71
[33] Zhang Q, Yue P, Gong L X 2006 Chin. Phys. 15 35
[34] Zhang J W, Wang D X, Wu R H 2008 Acta Phys. Sin. 57 2021 (in Chinese) [张建文、王旦霞、 吴润衡 2008 57 2021]
[35] He J H 2002 Approximate Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Publisher) (in Chinese) [何吉欢 2002 工程和科学中的近似非线性分析方法(郑州:河南科学技术出版社)]
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[1] McPhaden M J, Zhang D 2002 Nature 415 603
[2] Gu D F, Philander S G H 1994 Science 275 805.
[3] Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 10 (in Chinese) [刘式适、傅遵涛、刘式达、赵 强 2002 51 10]
[4] Pan L X, Zuo W M, Yan J R 1995 Acta Phys. Sin. 54 1 (in Chinese) [潘留仙、左伟明、颜家壬 2002 54 1]
[5] Pan L X, Liu J L, Li S S, Niu Z C, Feng S L, Zheng H Z 2002 Sci. Chin. 32A 556 (in Chinese) [潘留仙、刘金龙、李树深、牛智川、封松林、郑厚植 2002 中国科学 32A 556]
[6] Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林、董文杰、贾晓静、曹鸿兴 2002 51 1181]
[7] Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林、戴新刚、王爱慧、丑纪范 2001 50 606]
[8] Lin W T, Ji Z Z, Wang B, Zhang X 2002 Prog. Nat. Sci. 12 1326
[9] Wang L S, Xu D Y 2003 Sci. Chin. 32E 488 (in Chinese) [王林山、徐道义 2003 中国科学 32E 488]
[10] Mo J Q, Lin W T 2008 J. Sys. Sci. Complexity 20 119
[11] Mo J Q, Wang H 2007 Acta Ecologica Sin. 27 4366
[12] Mo J Q 2009 Chin. Phys. Lett. 26 060202
[13] Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese) [莫嘉琪 2009 58 2930]
[14] Mo J Q, Cheng Y 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、程 燕 2009 58 4379]
[15] Mo J Q 2009 Acta Phys. Sin.2009 58 695 (in Chinese) [莫嘉琪 2009 58 695]
[16] Mo J Q, Yao J S 2008 Acta Phys. Sin. 2008 57 7419 (in Chinese) [莫嘉琪、姚静荪 2008 57 7419]
[17] Mo J Q 2009 Sci. Chin. 52G 1007
[18] Mo J Q, Lin W T, Wang H 2007 Chin. Phys. 16 578
[19] Mo J Q, Lin W T, Wang H 2007 Prog. Nat. Sci. 17 230
[20] Mo J Q, Lin W T, Wang H 2008 Chin. Geographical Sci. 18 193
[21] Mo J Q, Lin W T 2008 Chin. Phys. 17 370
[22] Mo J Q, Lin W T 2008 Chin. Phys. 17 743
[23] Mo J Q 2010 Chin. Phys. 19 010203
[24] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. 19 030202
[25] Huang N N 1996 Theory of Solitons and Method of Perturbations (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [黄念宁 1996 孤子理论和扰动方法(上海:上海科技教育出版社)]
[26] Pan L X, Yan J R, Zhou G H 2001 Chin. Phys. 10 594
[27] Zheng Q, Yue P 2006 Chin. Phys. 15 35
[28] He H S, Chen J, Yang K Q 2005 Chin. Phys. 14 1926
[29] Lu F L, Chen C Y 2005 Chin. Phys. 14 463
[30] Zhang X A, Chen K, Duan Z I 2005 Chin. Phys. 14 42
[31] Teman R 1988 Infinite-Dimensional Dynamical System in Mechnica and Physica (New York: Springer)
[32] Zhu Z W, Lu Y 2000 J. Xhin. Quart. Math. 15 71
[33] Zhang Q, Yue P, Gong L X 2006 Chin. Phys. 15 35
[34] Zhang J W, Wang D X, Wu R H 2008 Acta Phys. Sin. 57 2021 (in Chinese) [张建文、王旦霞、 吴润衡 2008 57 2021]
[35] He J H 2002 Approximate Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Publisher) (in Chinese) [何吉欢 2002 工程和科学中的近似非线性分析方法(郑州:河南科学技术出版社)]
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