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采用了一个简单而有效的技巧,研究了一类非线性扰动Nizhnik-Novikov-Veselov系统. 首先引入一个相应典型系统的孤立波解. 然后利用同伦映射方法得到了原非线性扰动Nizhnik-Novikov-Veselov系统的近似解析解.
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关键词:
- 孤立波 /
- 扰动Nizhnik-Novikov-Veselov系统 /
- 同伦映射
The approximate analytic solution for a class of nonlinear disturbed Nizhnik-Novikov-Veselov system is considered by a simple and valid technique. We first introduce the approximate solution of a corresponding typical differential system. And then the approximate analytic solution for the original nonlinear disturbed Nizhnik-Novikov-Veselov system is obtained using the homotopic mapping method.[1] [1]McPhaden M J, Zhang D 2002 Nature 415 603
[2] [2]Gu D F, Philander S G H 1997 Science 275 805
[3] [3]Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) [马松华、 强继业、 方建平 2007 56 620]
[4] [4]Ma S H, Qiang J Y, Fang J P 2007 Comm. Theor. Phys. 48 662
[5] [5]Loutsenko I 2006 Comm. Math. Phys. 268 465
[6] [6]Gedalin M 1998 Phys. Plasmas 5 127
[7] [7]Parkes E J 2008 Chaos Solitons Fractals 38 154
[8] [8]Pan L S, Zou W M 2005 Acta Phys. Sin. 54 1 (in Chinese)[潘留仙、 左伟明 2005 54 1]
[9] [9]Pan L S, Liu J L, Li S S, Niu Z C, Feng S L, Zheng H Z 2002 Science in China A 32 556 (in Chinese) [潘留仙、 刘金龙、 李树深、 牛智川、 封松林、 郑厚值 2002 中国科学 A 32 556]
[10] ]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]
[11] ]Wang L S, Xu D Y 2003 Science in China E 32 488 (in Chinese) [王林山、 徐道义 2003 中国科学E 32 488]
[12] ]Wang M L 1995 Phys. Lett. A 199 169
[13] ]Wu G J, Han J H, Shi L M, Zhang M 2006 Acta Phys. Sin. 55 3858 (in Chinese) [吴国将、韩家骅、史良马、张苗 2006 55 3858]
[14] ]Li X Z, Li X Y, Zhang L Y, Zhang J L 2008 Acta Phys. Sin. 57 2203 (in Chinese) [李向正、李修勇、 赵丽英、 张金良 2008 57 2203]
[15] ]Li Z H, Zhang S Q 1997 Acta Math. Phys. Sin. 17 81 (in Chinese) [李志斌、 张善卿 1997 数学 17 81]
[16] ]Gao L, Xu W, Tang Y N, Shen J W 2007 Acta Phys. Sin. 56 1860 (in Chinese) [高亮、 徐伟、唐亚宁、 申建伟 2007 56 1860]
[17] ]Ma S H, Wu X H, Fang J P, Zhang X L 2008 Acta Phys. Sin. 57 11 (in Chinese) [马松华、 吴小红、 方建平、 郑春龙 2008 57 11]
[18] ]Bekir A 2008 Phys. Lett. A 372 2254
[19] ]Li B Q, Ma Y L 2009 Acta Phys. Sin. 58 4373 (in Chinese) [李帮庆、 马玉兰 2009 58 4373]
[20] ]Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York,CRC Press Co)
[21] ]He J H 2002 Approximate Analytical Methods in Engineering and Sciences (Shengzhou: Henan Science and Technology Press) (in Chinese) [何吉欢 2002 工程和科学计算中的近似非线性分析方法 (郑州 河南科学技术出版社)]
[22] ]Graef J R, Kong L 2008 Math. Proc.Camb. Philos. Soc. 145 489
[23] ]Hovhannisyan G, Vulanovic R 2008 Nonlinear Stud. 15 297
[24] ]Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392
[25] ]Ramos M, 2009 J. Math. Anal. Appl. 352 246
[26] ]Mo J Q, Zhu J, Wang H 2003 Prog. Nat. Sci. 13 768
[27] ]Mo J Q 2009 Chin. Phys. Lett. 26 060202-1
[28] ]Mo J Q, Cheng Yan 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、程燕 2009 58 4379]
[29] ]Mo J Q 2009 Science in China, G 52 1007
[30] ]Mo J Q, Lin W T, Lin Y H 2007 Acta Phys. Sin. 56 3127 (in Chinese) [莫嘉琪、 林万涛、 林一骅 2007 56 3127]
[31] ]Mo J Q, Lin W T 2008 Acta Phys. Sin. 57 6689 (in Chinese) [莫嘉琪、 林万涛 2008 57 6689]
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[1] [1]McPhaden M J, Zhang D 2002 Nature 415 603
[2] [2]Gu D F, Philander S G H 1997 Science 275 805
[3] [3]Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) [马松华、 强继业、 方建平 2007 56 620]
[4] [4]Ma S H, Qiang J Y, Fang J P 2007 Comm. Theor. Phys. 48 662
[5] [5]Loutsenko I 2006 Comm. Math. Phys. 268 465
[6] [6]Gedalin M 1998 Phys. Plasmas 5 127
[7] [7]Parkes E J 2008 Chaos Solitons Fractals 38 154
[8] [8]Pan L S, Zou W M 2005 Acta Phys. Sin. 54 1 (in Chinese)[潘留仙、 左伟明 2005 54 1]
[9] [9]Pan L S, Liu J L, Li S S, Niu Z C, Feng S L, Zheng H Z 2002 Science in China A 32 556 (in Chinese) [潘留仙、 刘金龙、 李树深、 牛智川、 封松林、 郑厚值 2002 中国科学 A 32 556]
[10] ]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]
[11] ]Wang L S, Xu D Y 2003 Science in China E 32 488 (in Chinese) [王林山、 徐道义 2003 中国科学E 32 488]
[12] ]Wang M L 1995 Phys. Lett. A 199 169
[13] ]Wu G J, Han J H, Shi L M, Zhang M 2006 Acta Phys. Sin. 55 3858 (in Chinese) [吴国将、韩家骅、史良马、张苗 2006 55 3858]
[14] ]Li X Z, Li X Y, Zhang L Y, Zhang J L 2008 Acta Phys. Sin. 57 2203 (in Chinese) [李向正、李修勇、 赵丽英、 张金良 2008 57 2203]
[15] ]Li Z H, Zhang S Q 1997 Acta Math. Phys. Sin. 17 81 (in Chinese) [李志斌、 张善卿 1997 数学 17 81]
[16] ]Gao L, Xu W, Tang Y N, Shen J W 2007 Acta Phys. Sin. 56 1860 (in Chinese) [高亮、 徐伟、唐亚宁、 申建伟 2007 56 1860]
[17] ]Ma S H, Wu X H, Fang J P, Zhang X L 2008 Acta Phys. Sin. 57 11 (in Chinese) [马松华、 吴小红、 方建平、 郑春龙 2008 57 11]
[18] ]Bekir A 2008 Phys. Lett. A 372 2254
[19] ]Li B Q, Ma Y L 2009 Acta Phys. Sin. 58 4373 (in Chinese) [李帮庆、 马玉兰 2009 58 4373]
[20] ]Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York,CRC Press Co)
[21] ]He J H 2002 Approximate Analytical Methods in Engineering and Sciences (Shengzhou: Henan Science and Technology Press) (in Chinese) [何吉欢 2002 工程和科学计算中的近似非线性分析方法 (郑州 河南科学技术出版社)]
[22] ]Graef J R, Kong L 2008 Math. Proc.Camb. Philos. Soc. 145 489
[23] ]Hovhannisyan G, Vulanovic R 2008 Nonlinear Stud. 15 297
[24] ]Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392
[25] ]Ramos M, 2009 J. Math. Anal. Appl. 352 246
[26] ]Mo J Q, Zhu J, Wang H 2003 Prog. Nat. Sci. 13 768
[27] ]Mo J Q 2009 Chin. Phys. Lett. 26 060202-1
[28] ]Mo J Q, Cheng Yan 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、程燕 2009 58 4379]
[29] ]Mo J Q 2009 Science in China, G 52 1007
[30] ]Mo J Q, Lin W T, Lin Y H 2007 Acta Phys. Sin. 56 3127 (in Chinese) [莫嘉琪、 林万涛、 林一骅 2007 56 3127]
[31] ]Mo J Q, Lin W T 2008 Acta Phys. Sin. 57 6689 (in Chinese) [莫嘉琪、 林万涛 2008 57 6689]
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