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The auxiliary equation method is used to construct the finite new exact solutions of nonlinear evolution equations. To search for infinite sequence soliton-like exact solutions of nonlinear evolution equations, characteristics of constructivity and mechanization of auxiliary equation method are analyzed and summarized. Therefore, the quasi-Bcklund transformation between new solutions of a kind of auxiliary equation with Riccati equation is presented, then (2+1)-dimensional modified dispersive water-wave system is taken as an applicable example to find infinite sequence soliton-like new exact solutions by choosing two kinds of formal solutions of nonlinear evolution equations with the help of symbolic computation system Mathematica, where included are the infinite sequence smooth soliton-like solutions, compact soliton solutions and peak soliton-like solutions.
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Keywords:
- auxiliary equation /
- nonlinear evolution equation /
- Bcklund transformation /
- soliton-like new exact solution
[1] Fan E G 2000 Phys. Lett. A 277 212
[2] [3] Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[4] [5] Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin. Phys. 12 1
[6] Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
[7] [8] [9] Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[10] [11] Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[12] [13] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[14] Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
[15] [16] Xie F D,Yuan Z T 2005 Commun. Theor. Phys. (Beijing) 43 39
[17] [18] Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 647
[19] [20] [21] LU Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[22] Xie F D, Gao X S 2004 Commun. Theor. Phys.(Beijing) 41 353
[23] [24] [25] Chen Y, Li B 2004 Commun. Theor. Phys. (Beijing) 41 1
[26] Ma S H, Fang J P, Zhu H P 2007 Acta Phys. Sin. 56 4319 (in Chinese) [马松华, 方建平, 朱海平 2007 56 4319]
[27] [28] Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [马松华, 吴小红, 方建平, 郑春龙 2008 57 11]
[29] [30] [31] Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 1569(in Chinese)[李德生, 张鸿庆 2003 52 1569]
[32] Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[33] [34] Wang Z,Li D S, Lu H F, Zhang H Q 2005 Chin. Phys. 14 2158
[35] [36] Wang Z, Zhang H Q 2006 Chin. Phys. 15 2210
[37] [38] [39] Li D S, Zhang H Q 2006 Acta Phys. Sin. 55 1565(in Chinese) [李德生, 张鸿庆 2006 55 1565]
[40] [41] Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[42] Lu D C, Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617(in Chinese)[卢殿臣, 洪宝剑, 田立新 2006 55 5617]
[43] [44] Boiti M 1987 Inverse Problems 3 37
[45] [46] Durovsky V G, Konopelchenko E G 1994 Phys. A 27 4619
[47] [48] Radha R, Lakshmanan M 1997 Math. Phys. 38 292
[49] [50] Radha R, Lakshmanan M 1999 Chaos, Solitons Fractals 10 1821
[51] -
[1] Fan E G 2000 Phys. Lett. A 277 212
[2] [3] Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[4] [5] Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin. Phys. 12 1
[6] Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
[7] [8] [9] Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[10] [11] Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[12] [13] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[14] Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
[15] [16] Xie F D,Yuan Z T 2005 Commun. Theor. Phys. (Beijing) 43 39
[17] [18] Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 647
[19] [20] [21] LU Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[22] Xie F D, Gao X S 2004 Commun. Theor. Phys.(Beijing) 41 353
[23] [24] [25] Chen Y, Li B 2004 Commun. Theor. Phys. (Beijing) 41 1
[26] Ma S H, Fang J P, Zhu H P 2007 Acta Phys. Sin. 56 4319 (in Chinese) [马松华, 方建平, 朱海平 2007 56 4319]
[27] [28] Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [马松华, 吴小红, 方建平, 郑春龙 2008 57 11]
[29] [30] [31] Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 1569(in Chinese)[李德生, 张鸿庆 2003 52 1569]
[32] Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[33] [34] Wang Z,Li D S, Lu H F, Zhang H Q 2005 Chin. Phys. 14 2158
[35] [36] Wang Z, Zhang H Q 2006 Chin. Phys. 15 2210
[37] [38] [39] Li D S, Zhang H Q 2006 Acta Phys. Sin. 55 1565(in Chinese) [李德生, 张鸿庆 2006 55 1565]
[40] [41] Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[42] Lu D C, Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617(in Chinese)[卢殿臣, 洪宝剑, 田立新 2006 55 5617]
[43] [44] Boiti M 1987 Inverse Problems 3 37
[45] [46] Durovsky V G, Konopelchenko E G 1994 Phys. A 27 4619
[47] [48] Radha R, Lakshmanan M 1997 Math. Phys. 38 292
[49] [50] Radha R, Lakshmanan M 1999 Chaos, Solitons Fractals 10 1821
[51]
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