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The method of combining function transformations with auxiliary equation is presented to search for new infinite sequence soliton-like solutions of Camassa-Holm-r (CH-r) equation. And many new conclusions are obtained. Step one,according to some function transformations, CH-r equation is changed into the solvable ordinary differential equation. Step two, new infinite sequence soliton-like solutions of CH-r equation are constructed by applying new solutions and Bäcklund transformation of the solvable ordinary differential equation.
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Keywords:
- function transformation /
- CH-r equation /
- solvable ordinary differential equation /
- new infinite sequence soliton-like solutions
[1] Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[2] Tian L X, Xu G, Liu Z R 2002 Appl. Math. Mech. 23 497 (in Chinese) [田立新, 许刚, 刘曾荣 2002 应用数学和力学 23 497]
[3] Alber M S, Camassa R 1994 Lett. Math. Phys. 32 137
[4] Clarkson P A, Mansfield E L, Priestley T J 1997 Math. Comput. Model. 25 195
[5] Xin Z P, Zhang P 2000 Comm. Pure. Appl. Math. 53 1411
[6] Fisher M, Schiff J 1999 Phys. Lett. A 259 371
[7] Constantin A, Atrauss W A 2000 Comm. Pure. Appl. Math. 53 603
[8] Boyd J P 1997 Appl. Math. Comput. 81 173
[9] Guo B L, Liu Z R 2003 China Sci. A 33 325 (in Chinese) [郭柏灵, 刘正荣 2003 中国科学A辑 33 325]
[10] Wang J M 2012 Acta. Phys. Sin. 61 080201 (in Chinese) [王军民 2012 61 080201]
[11] Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[12] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[13] Gepree K A, Omran S 2012 Chin. Phys. B 21 110204
[14] Zhang S 2007 Phys. Lett. A 368 470
[15] Pan Z H, Ma S H, Fang J P 2010 Chin. Phys. B 19 100301
[16] Ma S H, Fang J P, Zheng C L 2008 Chin. Phys. B 17 2767
[17] Shi L F, Chen C S, Zhou X C 2011 Chin. Phys. B 20 100507
[18] L Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[19] Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. 43 585
[20] Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[21] Ma S H, Fang J P 2012 Acta Phys. Sin. 61 180505 (in Chinese) [马松华, 方建平 2012 61 180505]
[22] Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A 372 417
[23] Fu Z T, Liu S K, Liu S D 2003 Commun. Theor. Phys. (Beijing) 39 27
[24] Li B Q, Ma Y L 2009 Acta. Phys. Sin. 58 4373 (in Chinese) [李帮庆, 马玉兰 2009 58 4373]
[25] Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. (Beijing) 55 949
[26] Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. 19 080303
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[1] Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[2] Tian L X, Xu G, Liu Z R 2002 Appl. Math. Mech. 23 497 (in Chinese) [田立新, 许刚, 刘曾荣 2002 应用数学和力学 23 497]
[3] Alber M S, Camassa R 1994 Lett. Math. Phys. 32 137
[4] Clarkson P A, Mansfield E L, Priestley T J 1997 Math. Comput. Model. 25 195
[5] Xin Z P, Zhang P 2000 Comm. Pure. Appl. Math. 53 1411
[6] Fisher M, Schiff J 1999 Phys. Lett. A 259 371
[7] Constantin A, Atrauss W A 2000 Comm. Pure. Appl. Math. 53 603
[8] Boyd J P 1997 Appl. Math. Comput. 81 173
[9] Guo B L, Liu Z R 2003 China Sci. A 33 325 (in Chinese) [郭柏灵, 刘正荣 2003 中国科学A辑 33 325]
[10] Wang J M 2012 Acta. Phys. Sin. 61 080201 (in Chinese) [王军民 2012 61 080201]
[11] Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[12] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[13] Gepree K A, Omran S 2012 Chin. Phys. B 21 110204
[14] Zhang S 2007 Phys. Lett. A 368 470
[15] Pan Z H, Ma S H, Fang J P 2010 Chin. Phys. B 19 100301
[16] Ma S H, Fang J P, Zheng C L 2008 Chin. Phys. B 17 2767
[17] Shi L F, Chen C S, Zhou X C 2011 Chin. Phys. B 20 100507
[18] L Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[19] Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. 43 585
[20] Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[21] Ma S H, Fang J P 2012 Acta Phys. Sin. 61 180505 (in Chinese) [马松华, 方建平 2012 61 180505]
[22] Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A 372 417
[23] Fu Z T, Liu S K, Liu S D 2003 Commun. Theor. Phys. (Beijing) 39 27
[24] Li B Q, Ma Y L 2009 Acta. Phys. Sin. 58 4373 (in Chinese) [李帮庆, 马玉兰 2009 58 4373]
[25] Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. (Beijing) 55 949
[26] Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. 19 080303
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