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Novel loop-like solitons for generalized Vakhnenko equation |
Zhang Min (张旻)a, Ma Yu-Lan (马玉兰)a, Li Bang-Qing (李帮庆)a b |
a School of Science, Beijing Technology and Business University, Beijing 100048, China; b School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China |
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Abstract A nontraveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method. The solution includes an arbitrary function of an independent variable. Based on the solution, two hyperbolic functions are chosen to construct new solitons. Novel single-loop-like and double-loop-like solitons are found for the equation.
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Received: 03 July 2012
Revised: 03 September 2012
Accepted manuscript online:
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PACS:
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05.45.Yv
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(Solitons)
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03.65.Ge
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(Solutions of wave equations: bound states)
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Fund: Project supported by the Scientific Research Common Program of Beijing Municipal Commission of Education, China (Grant No. KM201010011001), PHR (Grant No. 201106206), the Funding Project for Innovation on Science, Technology and Graduate Education in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality, China (Grant Nos. 201098, PXM2012_-014213_000087, PXM2012_-014213_-000037, and PXM2012_-014213_-000079). |
Corresponding Authors:
Ma Yu-Lan
E-mail: mayl@th.btbu.edu.cn
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Cite this article:
Zhang Min (张旻), Ma Yu-Lan (马玉兰), Li Bang-Qing (李帮庆) Novel loop-like solitons for generalized Vakhnenko equation 2013 Chin. Phys. B 22 030511
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[1] |
Vakhnenko V O 1992 J. Math. Phys. A 25 4181
|
[2] |
Vakhnenko V O 1999 J. Math. Phys. 40 2011
|
[3] |
Parkes E J 1993 J. Phys. A 26 6469
|
[4] |
Vakhnenko V O and Parkes E J 1998 Nonlinearity 11 1457
|
[5] |
Vakhnenko V O, Parkes E J and Michtchenko A V 2000 Int. J. Differential Equations Appl. 1 429
|
[6] |
Morrison A J, Parkes E J and Vakhnenko V O 1999 Nonlinearity 12 1427
|
[7] |
Li J B 2007 Science in China Series A: Math. 50 773
|
[8] |
Li W A, Chen H and Zhang G C 2009 Chin. Phys. B 18 400
|
[9] |
Wu Y Y, Wang C and Liao S J 2005 Chaos Soliton. Fract. 23 1733
|
[10] |
Ma Y L and Li B Q 2010 J. Math. Phys. 51 063512
|
[11] |
Morrison A J and Parkes E J 2003 Chaos Soliton. Fract. 16 13
|
[12] |
Vakhnenko V O, Parkes E J and Morrison A J 2003 Chaos Soliton. Fract. 17 683
|
[13] |
Victor K K, Thomas B B and Kofane T C 2008 Chin. Phys. Lett. 25 425
|
[14] |
Mo J Q 2009 Chin. Phys. B 18 4608
|
[15] |
Liu Y P, Li Z B and Wang K C 2007 Chaos Soliton. Fract. 31 117
|
[16] |
Ma Y L, Li B Q and Wang C 2009 Appl. Math. Comput. 211 102
|
[17] |
Ma Y L and Li B Q 2010 Appl. Math. Comput. 216 2137
|
[18] |
Li B Q, Ma Y L and Sun J Z 2010 Appl. Math. Comput. 216 3522
|
[19] |
Ma Y L and Li B Q 2012 Appl. Math. Comput. 219 2212
|
[20] |
Fan E G 2002 Phys. Lett. A 300 243
|
[21] |
Zheng C L, Fang J P and Chen L Q 2005 Acta Phys. Sin. 54 676 (in Chinese)
|
[22] |
Fei J X and Zheng C L 2012 Chin. Phys. B 21 070304
|
[23] |
Zheng C L and Li Y 2012 Chin. Phys. B 21 070305
|
[24] |
Chen Y, Li B and Zhang H Q 2003 Chin. Phys. 12 940
|
[25] |
Yang Z, Ma S H and Fang J P 2011 Chin. Phys. B 20 040301
|
[26] |
Ma S H, Fang J P, Ren Q B and Yang Z 2012 Chin. Phys. B 21 050511
|
[27] |
Ma S H, Lei Y and Fang J P 2012 Acta Phys. Sin. 61 180505 (in Chinese)
|
[28] |
Zeng W L, Ma S H and Ren Q B 2012 Acta Phys. Sin. 61 110508 (in Chinese)
|
[29] |
Li B Q, Ma Y L and Xu M P 2010 Acta Phys. Sin. 59 1409 (in Chinese)
|
[30] |
Li B Q and Ma Y L 2010 Z. Naturforsch A 65a 518
|
[31] |
Li B Q and Ma Y L 2011 Commun. Nonlinear Sci. Numer. Simul. 16 144
|
[32] |
Wang M L Zhou Y B and Li Z B 1996 Phys. Lett. A 216 67
|
[33] |
Parkes E J 2007 Chaos Soliton. Fract. 31 602
|
[34] |
Li B Q, Ma Y L, Wang C, Xu M P and Li Y 2011 Acta Phys. Sin. 60 060203 (in Chinese)
|
[35] |
Yang P, Chen Y and Li Z B 2010 Commun. Theor. Phys. 53 1027
|
[36] |
Shen S F 2006 Acta Phys. Sin. 55 1016 (in Chinese)
|
[37] |
Sakovich A and Sakovich S 2006 J. Phys. A: Math. Gen. 39 L361
|
[38] |
Ma Y L and Li B Q 2012 J. Appl. Math. Comput. 40 683
|
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