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几类具有变系数的KdV型方程的孤波解 被引量：1

SOLITARY WAVE SOLUTIONS FOR KdV EQUATIONS WITH VARIABLE COEFFICIENTS
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摘要 利用齐次平衡法研究几类具有变系数的KdV型方程,获得了一些新的由双曲函数tanh和sech来表示的精确孤波解.该方法也适用于其它的非线性演化方程. Several exact solitary wave solutions,presented by the tanh and sech hyperbolic functions,for various KdV type equations with variable coefficients are obtained by using the homogeneous balance method.This method can also be used to other nonlinear evolution equations.
作者 吴楚芬 翁佩萱
机构地区 华南师范大学数学科学学院 上海交通大学数学系
出处 《华南师范大学学报（自然科学版）》 CAS 北大核心 2010年第4期15-18,共4页 Journal of South China Normal University(Natural Science Edition)
基金 教育部高等学校博士学科点专项科研基金项目(20094407110001) 广东省自然科学基金项目(10151063101000003)
关键词 KDV方程 变系数 tanh-sech函数方法 齐次平衡法 孤波解 KdV equation variable coefficient the tanh-sech function method homogeneous balance method solitary wave solution
分类号 O175.29 [理学—基础数学]
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参考文献18

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同被引文献14

  • 1KORTEWEG D,de VRIES D.On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves[J].The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science,1895,39(240):422-443.
  • 2SCOTT A,CHU F,MCLAUGHLIN D.The soliton: A new concept in applied science[J].Proceedings of the IEEE,1973,61(10):1443-1483.
  • 3MIURA R.The korteweg-devries equation: A survey of results[J].SIAM Review,1976,18(3):412-459.
  • 4LOU Shen-yue,TONG Bin,HU Heng-chun,et al.Coupled KdV equations derived from two-layer fluids[J].Journal of Physics A: Mathematical and General,2006,39(3):513-527.
  • 5WANG Ming-liang,WANG Yue-ming.A new b?cklund transformation and multi-soliton solutions to the KdV equation with general variable coefficients[J].Physics Letters A,2001,287(3/4):211-216.
  • 6PRADHAN K,PANIGRAHI P.Parametrically controlling solitary wave dynamics in the modified Korteweg-de Vries equation[J].Journal of Physics A: Mathematical and General,2006,39(20):L343-L348.
  • 7YAN Zhen-ya.The modified KdV equation with variable coefficients: Exact uni/bi-variable travelling wave-like solutions[J].Applied Mathematics and Computation,2008,203(1):106-112.
  • 8ZHOU Yu-bin,WANG Ming-liang,WANG Yue-ming.Periodic wave solutions to a coupled KdV equations with variable coefficients[J].Physics Letters A,2003,308(1):31-36.
  • 9WEN Zhen-shu,LIU Zheng-rong.Bifurcation of peakons and periodic cusp waves for the generalization of the camassa-holm equation[J].Nonlinear Analysis: Real World Applications,2011,12(3):1698-1707.
  • 10WEN Zhen-shu,LIU Zheng-rong,SONG Ming.New exact solutions for the classical drinfel’d-sokolov-wilson equation[J].Applied Mathematics and Computation,2009,215(6):2349-2358.

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华南师范大学学报（自然科学版）
2010年 第4期

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