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用动力系统分岔方法研究了一类非线性色散Boussinesq方程.在不同的参数条件下,给出了该方程具有隐函数形式的孤立波解的解析表达式.数值模拟进一步验证了所得结果的正确性.
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关键词:
- 非线性色散Boussinesq方程 /
- 分岔方法 /
- 同宿轨道 /
- 隐式孤立波解
By applying the bifurcation method of dynamical systems to a class of nonlinear dispersive Boussinesq equations, the analytic expressions of implicit solitary wave solutions are obtained under different parameter conditions. Numerical simulations are given to show the correctness of our results.-
Keywords:
- nonlinear dispersive Boussinesq equation /
- bifurcation method /
- homoclinic orbit /
- implicit solitary wave solutions
[1] Ablowitz M J, Clarkson P A 1991 Soliton, Nolinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
[2] Wu Y Q 2010 Acta Phys. Sin. 59 1403 (in Chinese)[吴勇旗 2010 59 1403]
[3] Huang W H 2009 Chin. Phys. B 18 3163
[4] Zeng X, Zhang H Q 2005 Acta Phys. Sin. 54 1476 (in Chinese)[曾 昕、 张鸿庆 2005 54 1476]
[5] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese)[范恩贵、 张鸿庆 1998 47 353]
[6] Shi Y R, Yang H J 2010 Acta Phys. Sin. 59 67 (in Chinese)[石玉仁、 杨红娟 2010 59 67]
[7] Li J B, Zhan Y 2009 Nonlinear Anal.: Real World Appl. 10 2502
[8] Guo B L, Liu Z R 2005 Chaos Solitons Fract. 23 1451
[9] Shen J W, Xu W, Lei Y M 2005 Chaos Solitons Fract. 23 117
[10] Bi Q S 2005 Phys. Lett. A 344 361
[11] Li Z B, Zhang S Q 1997 Acta Math. Sci. 17 81 (in Chinese)[李志斌、 张善卿 1997 数学 17 81]
[12] Yan Z Y 2003 Chaos Solitons Fract. 18 299
[13] Wazwaz A M 2004 Appl. Math. Comput. 154 713
[14] Fan E G 2000 Phys. Lett. A 277 212
[15] 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]
[16] Zhang L J, Chen L Q, Huo X W 2007 Nolinear Anal. 67 3276
[17] Yan Z Y 2002 Chaos Solitons Fract. 14 1151
[18] Zhu Y 2006 Nolinear Anal. 64 901
[19] Zhu Y 2005 Chaos Solitons Fract. 26 897
[20] Zhu Y 2007 Chaos Solitons Fract. 32 768
[21] Zhu Y 2006 Chaos Solitons Fract. 30 1238
[22] Guckenheimer J, Holmes P J 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (New York: Springer-Verlag)
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[1] Ablowitz M J, Clarkson P A 1991 Soliton, Nolinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
[2] Wu Y Q 2010 Acta Phys. Sin. 59 1403 (in Chinese)[吴勇旗 2010 59 1403]
[3] Huang W H 2009 Chin. Phys. B 18 3163
[4] Zeng X, Zhang H Q 2005 Acta Phys. Sin. 54 1476 (in Chinese)[曾 昕、 张鸿庆 2005 54 1476]
[5] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese)[范恩贵、 张鸿庆 1998 47 353]
[6] Shi Y R, Yang H J 2010 Acta Phys. Sin. 59 67 (in Chinese)[石玉仁、 杨红娟 2010 59 67]
[7] Li J B, Zhan Y 2009 Nonlinear Anal.: Real World Appl. 10 2502
[8] Guo B L, Liu Z R 2005 Chaos Solitons Fract. 23 1451
[9] Shen J W, Xu W, Lei Y M 2005 Chaos Solitons Fract. 23 117
[10] Bi Q S 2005 Phys. Lett. A 344 361
[11] Li Z B, Zhang S Q 1997 Acta Math. Sci. 17 81 (in Chinese)[李志斌、 张善卿 1997 数学 17 81]
[12] Yan Z Y 2003 Chaos Solitons Fract. 18 299
[13] Wazwaz A M 2004 Appl. Math. Comput. 154 713
[14] Fan E G 2000 Phys. Lett. A 277 212
[15] 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]
[16] Zhang L J, Chen L Q, Huo X W 2007 Nolinear Anal. 67 3276
[17] Yan Z Y 2002 Chaos Solitons Fract. 14 1151
[18] Zhu Y 2006 Nolinear Anal. 64 901
[19] Zhu Y 2005 Chaos Solitons Fract. 26 897
[20] Zhu Y 2007 Chaos Solitons Fract. 32 768
[21] Zhu Y 2006 Chaos Solitons Fract. 30 1238
[22] Guckenheimer J, Holmes P J 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (New York: Springer-Verlag)
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