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We numerically investigate the interaction between multi-compactons of the K(m,n,p) equation by a finite difference scheme that is of the second-order accuracy and absolutely stable in linearization sense. By adding an artificial dissipation term, it works well for preventing the break-up phenomena of the numerical solutions. Firstly, we simulate the long-time evolution behaviors of the single-compacton to verify the validity of the numerical method. It is shown that the numerical method is effective for solving this problem. Secondly, we study the nonlinear interaction between two-compacton and three-compacton by this numerical method. The numerical results indicate that the wave-frame and wave-velocity after collision are nearly the same as before collision. However, compacton-anticompacton pair induced behind the wave arises with small amplitudes.
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Keywords:
- K(m,n,p) equation /
- compacton /
- finite difference scheme
[1] Abdul-Majid W 2007 Appl. Math. Comput. 184 1002
[2] Li H M, Lou S Y 2002 J. Liaoning Normal Univ. (Natural Science Edition) 25 23(in Chinese)[李画眉, 楼森岳 2002 辽宁师范大学学报 (自然科学版) 25 23]
[3] Yin J L, Fan Y Q, Zhang J, Tian L X 2011 Acta Phys. Sin. 60 080201(in Chinese)[殷久利, 樊玉琴, 张娟, 田立新 2011 物理学报 60 080201]
[4] Xu G Q 2013 Chin. Phys. B 22 050203
[5] Wu J L, Lou S Y 2012 Chin. Phys. B 12 120204
[6] Jia M, Wang J Y, Lou S Y 2009 Chin. Phys. Lett. 26 020201
[7] Lei Y, Lou S Y 2013 Chin. Phys. Lett. 30 060202
[8] Yin J L, Tian L X 2003 J. Jiangsu Univ. (Natural Science Edition) 24 9(in Chinese)[殷久利, 田立新 2003 江苏大学学报 (自然科学版) 24 9]
[9] Abassy T A, El-Tawil M, Kamel H 2004 Internat. J. Nonlinear Sci. Numer. Simul. 5 327
[10] Cooper F, Hyman J, Khare A 2001 Phys. Rev. E 64 1
[11] Wazwaz A M 2002 Appl. Math. Comput. 133 213
[12] Rosenau P, Hyman J M 1993 Phys. Rev. Lett. 70 564
[13] Zhou Y B, Wang M L, Wang Y M 2003 Phys. Lett. A 308 31
[14] Abbasbandy S 2007 Phys. Lett. A 361 478
[15] Abassy T A, El-Tawil M A, El-Zoheiry H 2007 Comput. Math. Appl. 54 940
[16] Levy D, Shu C W, Yan J 2004 J. Comput. Phys. 196 751
[17] He B, Meng Q 2010 Appl. Math. Comput. 217 1697
[18] Zheng C L, Chen L Q, Zhang J F 2005 Phys. Lett. A 340 397
[19] Wang Y F, Lou S Y, Qian X M 2010 Chin. Phys. B 19 050202
[20] Yao R X, Jiao X Y, Lou S Y 2009 Chin. Phys. B 18 1821
[21] Lou S Y, Ruan H Y 2001 J. Phys. A 34 305
[22] Soliman A A 2006 Chaos, Soliton. Fract. 29 294
[23] Ganji D D, Rafei M 2006 Phys. Lett. A 356 131
[24] Abbasbandy S, Zakaria F S 2008 Nonlinear Dyn. 51 83
[25] Zhang S 2007 Phys. Lett. A 365 448
[26] Li X Z, Wang M L 2007 Phys. Lett. A 361 115
[27] Wazwaz A M 2002 Appl. Math. Comput. 133 229
[28] Rosenau P 2006 Phys. Lett. A 356 44
[29] Rosenau P 1997 Phys. Lett. A 230 305
[30] Dey B 1998 Phys. Rev. E 57 4733
[31] Tian L X, Yin J L 2005 Chaos, Soliton. Fract. 23 159
[32] Abassy T A, Zoheiry H E, El-Tawil M A 2009 J. Comput. Appl. Math. 232 388
[33] Lu J F, Guan Z 2003 Numerical Methods for Solving Partial Differential Equations (Beijing: Tsinghua University Press) pp28-37 (in Chinese)[陆金甫, 关治 2003 偏微分方程数值解法 (北京: 清华大学出版社) 第28-37页]
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[1] Abdul-Majid W 2007 Appl. Math. Comput. 184 1002
[2] Li H M, Lou S Y 2002 J. Liaoning Normal Univ. (Natural Science Edition) 25 23(in Chinese)[李画眉, 楼森岳 2002 辽宁师范大学学报 (自然科学版) 25 23]
[3] Yin J L, Fan Y Q, Zhang J, Tian L X 2011 Acta Phys. Sin. 60 080201(in Chinese)[殷久利, 樊玉琴, 张娟, 田立新 2011 物理学报 60 080201]
[4] Xu G Q 2013 Chin. Phys. B 22 050203
[5] Wu J L, Lou S Y 2012 Chin. Phys. B 12 120204
[6] Jia M, Wang J Y, Lou S Y 2009 Chin. Phys. Lett. 26 020201
[7] Lei Y, Lou S Y 2013 Chin. Phys. Lett. 30 060202
[8] Yin J L, Tian L X 2003 J. Jiangsu Univ. (Natural Science Edition) 24 9(in Chinese)[殷久利, 田立新 2003 江苏大学学报 (自然科学版) 24 9]
[9] Abassy T A, El-Tawil M, Kamel H 2004 Internat. J. Nonlinear Sci. Numer. Simul. 5 327
[10] Cooper F, Hyman J, Khare A 2001 Phys. Rev. E 64 1
[11] Wazwaz A M 2002 Appl. Math. Comput. 133 213
[12] Rosenau P, Hyman J M 1993 Phys. Rev. Lett. 70 564
[13] Zhou Y B, Wang M L, Wang Y M 2003 Phys. Lett. A 308 31
[14] Abbasbandy S 2007 Phys. Lett. A 361 478
[15] Abassy T A, El-Tawil M A, El-Zoheiry H 2007 Comput. Math. Appl. 54 940
[16] Levy D, Shu C W, Yan J 2004 J. Comput. Phys. 196 751
[17] He B, Meng Q 2010 Appl. Math. Comput. 217 1697
[18] Zheng C L, Chen L Q, Zhang J F 2005 Phys. Lett. A 340 397
[19] Wang Y F, Lou S Y, Qian X M 2010 Chin. Phys. B 19 050202
[20] Yao R X, Jiao X Y, Lou S Y 2009 Chin. Phys. B 18 1821
[21] Lou S Y, Ruan H Y 2001 J. Phys. A 34 305
[22] Soliman A A 2006 Chaos, Soliton. Fract. 29 294
[23] Ganji D D, Rafei M 2006 Phys. Lett. A 356 131
[24] Abbasbandy S, Zakaria F S 2008 Nonlinear Dyn. 51 83
[25] Zhang S 2007 Phys. Lett. A 365 448
[26] Li X Z, Wang M L 2007 Phys. Lett. A 361 115
[27] Wazwaz A M 2002 Appl. Math. Comput. 133 229
[28] Rosenau P 2006 Phys. Lett. A 356 44
[29] Rosenau P 1997 Phys. Lett. A 230 305
[30] Dey B 1998 Phys. Rev. E 57 4733
[31] Tian L X, Yin J L 2005 Chaos, Soliton. Fract. 23 159
[32] Abassy T A, Zoheiry H E, El-Tawil M A 2009 J. Comput. Appl. Math. 232 388
[33] Lu J F, Guan Z 2003 Numerical Methods for Solving Partial Differential Equations (Beijing: Tsinghua University Press) pp28-37 (in Chinese)[陆金甫, 关治 2003 偏微分方程数值解法 (北京: 清华大学出版社) 第28-37页]
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