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一类广义非线性扰动色散方程孤立波的近似解

莫嘉琪 陈贤峰

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一类广义非线性扰动色散方程孤立波的近似解

莫嘉琪, 陈贤峰

Approximate solution of solitary wave for a class of generalized nonlinear disturbed dispersive equation

Mo Jia-Qi, Chen Xian-Feng
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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色散方程. 首先引入求解相应典型方程的孤立波解. 然后利用同伦映射方法得到了原非线性扰动色散方程奇异孤立波的近似解.
    The approximate solution for a class of nonlinear disturbed dispersive equation is considered using a simple and valid technique. We first introduce the solitary wave solution of the corresponding typical differential equation, and then the approximate solution of the singular solitary wave for an original nonlinear disturbed dispersive equation is obtained using the homotopic mapping method.
    • 基金项目: 国家自然科学基金(批准号:40876010),中国科学院知识创新工程重要方向项目(批准号:KZCX2-YW-Q03-08),公益性行业(气象)科研专项(批准号:GYHY200806010),LASG国家重点实验室专项经费,上海市教育委员会E-研究院建设计划项目(批准号:E03004)和浙江省自然科学基金(批准号:6090104)资助的课题.
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    [5]Loutsenko I 2006 Comm. Math. Phys. 268 465

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    [7]Parkes E J 2008 Chaos Solitons Fractals 38 154

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    [8]Wang M L 1995 Phys. Lett. A 199 169

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    [9]Sirendaoreji J S 2003 Phys. Lett. A309 387

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    [10]Yang J R,Mao J J 2008 Chin. Phys. Lett. 25 1527

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    [14]Lu D C,Hong B J,Tian L X 2006 Acta Phys. Sin. 55 5617 (in Chinese)[卢殿臣、烘宝剑、田立新 2006 物理学报 55 5617]

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    [15]Tapgetusang,Sirendaoerji 2009 Acta Phys. Sin. 58 2121 (in Chinese)[套格图桑、斯仁道尔吉 2009 物理学报 58 2121]

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    [16]Rosennau P,Hyman M 1933 Phys. Rev. Lett. 70 564

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    [18]Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method(New York,CRC Press Co)

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    [19]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分析方法 (郑州 河南科学技术出版社)]

    [20]

    [20]Hovhannisyan G.,Vulanovic R 2008 Nonlinear Stud. 15 297

    [21]

    [21]Graef J R,Kong L 2008 Math. Proc.Camb. Philos. Soc. 145 489

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    [24]Mo J Q 1989 Science in ChinaSer A 32 1306

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    [25]Mo J Q,Lin W T 2008 J. Sys. Sci. & Complexity 20 119

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    [26]Mo J Q,Wang H 2007 Acta Ecologica Sinica 27 4366

    [27]

    [27]Mo J Q,Zhu J,Wang H 2003 Prog. Nat. Sci. 13 768

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    [28]Mo J Q,Zhang W J,He M 2007 Acta Phys. Sin. 56 1843 (in Chinese)[莫嘉琪、张伟江、何 铭 2006 物理学报 56 1843]

    [29]

    [29]Mo J Q,Zhang W J,Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese)[莫嘉琪、张伟江、陈贤峰 2007 物理学报 56 6169]

    [30]

    [30]Mo J Q,Yao J S 2008 Acta Phys. Sin. 57 7419 (in Chinese)[莫嘉琪、姚静荪 2008 物理学报 57 7419]

    [31]

    [31]Mo J Q 2009 Chin. Phys. Lett. 26 010204-1

    [32]

    [32]Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese)[莫嘉琪 2009 物理学报 58 695]

    [33]

    [33]Mo J Q 2009 Chin. Phys. Lett. 26 060202-1

    [34]

    [34]Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese)[莫嘉琪 2009 物理学报 58 2930]

    [35]

    [35]Mo J Q 2009 Science in China,Ser. G 52 1007

    [36]

    [36]Mo J Q,Zhang W J,He M 2006 Acta Phys. Sin. 55 3233 (in Chinese)[莫嘉琪、张伟江、何铭 2006 物理学报 55 3233]

    [37]

    [37]Mo J Q,Lin W T,Wang H 2008 Chin. Geographical Sci. 18 193

    [38]

    [38]Mo J Q,Lin W T,Wang H 2007 Prog. Nat. Sci. 17 230

    [39]

    [39]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 物理学报 56 1843]

    [40]

    [40]Mo J Q,Lin W T,Wang H 2007 Chin. Phys. 16 951

    [41]

    [41]Mo J Q,Lin W T 2008 Chin. Phys. B 17 370

    [42]

    [42]Mo J Q,Lin W T 2008 Chin. Phys. B 17 743

  • [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 物理学报 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]Wang M L 1995 Phys. Lett. A 199 169

    [9]

    [9]Sirendaoreji J S 2003 Phys. Lett. A309 387

    [10]

    [10]Yang J R,Mao J J 2008 Chin. Phys. Lett. 25 1527

    [11]

    [11]Gao Y,Tang X Y 2007 Commum. Theor. Phys. 48 961

    [12]

    [12]Yang J R,Mao J J 2008 Chin. Phys. B 17 4337

    [13]

    [13]Pan L X,Zuo W M,Yan J R 2005 Acta Phys. Sin. 54 1 (in Chinese)[潘留仙、左伟明、颜家壬 2005 物理学报 54 1]

    [14]

    [14]Lu D C,Hong B J,Tian L X 2006 Acta Phys. Sin. 55 5617 (in Chinese)[卢殿臣、烘宝剑、田立新 2006 物理学报 55 5617]

    [15]

    [15]Tapgetusang,Sirendaoerji 2009 Acta Phys. Sin. 58 2121 (in Chinese)[套格图桑、斯仁道尔吉 2009 物理学报 58 2121]

    [16]

    [16]Rosennau P,Hyman M 1933 Phys. Rev. Lett. 70 564

    [17]

    [17]Yin L J,Tian L X 2009 Acta Phys. Sin. 58 3632 (in Chinese)[殷利久、田立新 2009 物理学报 58 3632]

    [18]

    [18]Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method(New York,CRC Press Co)

    [19]

    [19]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分析方法 (郑州 河南科学技术出版社)]

    [20]

    [20]Hovhannisyan G.,Vulanovic R 2008 Nonlinear Stud. 15 297

    [21]

    [21]Graef J R,Kong L 2008 Math. Proc.Camb. Philos. Soc. 145 489

    [22]

    [22]Barbu L,Cosma E 2009 J. Math. Anal. Appl. 351 392

    [23]

    [23]Ramos M 2009 J. Math. Anal. Appl. 352 246

    [24]

    [24]Mo J Q 1989 Science in ChinaSer A 32 1306

    [25]

    [25]Mo J Q,Lin W T 2008 J. Sys. Sci. & Complexity 20 119

    [26]

    [26]Mo J Q,Wang H 2007 Acta Ecologica Sinica 27 4366

    [27]

    [27]Mo J Q,Zhu J,Wang H 2003 Prog. Nat. Sci. 13 768

    [28]

    [28]Mo J Q,Zhang W J,He M 2007 Acta Phys. Sin. 56 1843 (in Chinese)[莫嘉琪、张伟江、何 铭 2006 物理学报 56 1843]

    [29]

    [29]Mo J Q,Zhang W J,Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese)[莫嘉琪、张伟江、陈贤峰 2007 物理学报 56 6169]

    [30]

    [30]Mo J Q,Yao J S 2008 Acta Phys. Sin. 57 7419 (in Chinese)[莫嘉琪、姚静荪 2008 物理学报 57 7419]

    [31]

    [31]Mo J Q 2009 Chin. Phys. Lett. 26 010204-1

    [32]

    [32]Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese)[莫嘉琪 2009 物理学报 58 695]

    [33]

    [33]Mo J Q 2009 Chin. Phys. Lett. 26 060202-1

    [34]

    [34]Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese)[莫嘉琪 2009 物理学报 58 2930]

    [35]

    [35]Mo J Q 2009 Science in China,Ser. G 52 1007

    [36]

    [36]Mo J Q,Zhang W J,He M 2006 Acta Phys. Sin. 55 3233 (in Chinese)[莫嘉琪、张伟江、何铭 2006 物理学报 55 3233]

    [37]

    [37]Mo J Q,Lin W T,Wang H 2008 Chin. Geographical Sci. 18 193

    [38]

    [38]Mo J Q,Lin W T,Wang H 2007 Prog. Nat. Sci. 17 230

    [39]

    [39]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 物理学报 56 1843]

    [40]

    [40]Mo J Q,Lin W T,Wang H 2007 Chin. Phys. 16 951

    [41]

    [41]Mo J Q,Lin W T 2008 Chin. Phys. B 17 370

    [42]

    [42]Mo J Q,Lin W T 2008 Chin. Phys. B 17 743

计量
  • 文章访问数:  6188
  • PDF下载量:  1366
  • 被引次数: 0
出版历程
  • 收稿日期:  2009-06-21
  • 修回日期:  2009-06-29
  • 刊出日期:  2010-03-15

一类广义非线性扰动色散方程孤立波的近似解

  • 1. (1)安徽师范大学数学系,芜湖 241000;上海高校计算科学院E-研究院上海交通大学研究所,上海 200240; (2)上海交通大学数学系,上海 200240;上海高校计算科学院E-研究院上海交通大学研究所,上海 200240
    基金项目: 国家自然科学基金(批准号:40876010),中国科学院知识创新工程重要方向项目(批准号:KZCX2-YW-Q03-08),公益性行业(气象)科研专项(批准号:GYHY200806010),LASG国家重点实验室专项经费,上海市教育委员会E-研究院建设计划项目(批准号:E03004)和浙江省自然科学基金(批准号:6090104)资助的课题.

摘要: 采用了一个简单而有效的技巧, 研究了一类非线性扰动色散方程. 首先引入求解相应典型方程的孤立波解. 然后利用同伦映射方法得到了原非线性扰动色散方程奇异孤立波的近似解.

English Abstract

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