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利用符号计算软件Maple，在一个新的广义的Riccati方程有理展开法的帮助下，得到了关于复合的KdV系统及广义的KdV-Burgers系统的几个新的更广义类型的精确解. 该方法还可被应用到其他非线性发展方程中去.
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关键词:
- 新的广义的Riccati方程有理展开法 /
- 复合的KdV系统 /
- 广义的KdV-Burgers系统 /
- 符号计算
With the aid of symbolic computation system Maple, several new kinds of generalized exact solutions for the compound KdV system and extended KdV-Burgers system with nonlinear terms of any order are obtained by using a new generalize Riccati equation rational expansion method. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order.-
Keywords:
- generalized Riccati equation rational expansion method /
- compound KdV system with nonlinear terms of any order /
- extended KdV-Burgers system with nonlinear terms of any order /
- symbolic computation
[1] ［1］Ablowitz M J，Clarkson P A 1991 Solitons, nonlinear evolution equations and inverse scattering (New York: Cambridge University Press)
[2] ［2］Wadati M. J 1972 Phys. Soc. Jpn. 32 1681
[3] ［3］Hirota R 1971 Phys. Rev. Lett. 27 1192
[4] ［4］Lou S Y 2000 Phys. Lett. A 277 94
[5] ［5］Wang M L 1995 Phys. Lett. A 199 169
[6] ［6］Parkes E J，Duffy B R 1996 Comp. Phys. Commun. 98 288 Parkes E J，Duffy B R 1997 Phys. Lett. A 229 217
[7] ［7］Khater A H，Malfliet W， Callebaut D K， Kamel E S 2002 Chaos, Solitons and Fractals 14 513
[8] ［8］Fan E G 2000 Phys. Lett. A 277 212 Fan E G 2001 Phys. Lett. A 282 18
[9] ［9］Elwakil S A，El-labany S K，Zahran M A，Sabry R 2002 Phys.Lett. A 299 179
[10] ］Gao Y T，Tian B 2001 Comp. Phys.Commun. 133 158
[11] ］Wang Q，Chen Y，Zhang H Q 2005 Phys. Lett. A 340 411
[12] ］Wang J，Zhang X L，Song L N，Zhang H Q 2006 Appl.Math. Comput.182 1330
[13] ］Li Z B，Liu Y P 2002 Comp. Phys. Commun. 148 256
[14] ］Yan Z Y，Zhang H Q 1999 Phys. Lett. A 252 291
[15] ］Li B，Chen Y，Zhang H Q 2003 Chaos Solitons and Fractals 15 647
[16] ］Xie F D，Chen J，Lü Z S 2005 Commun. Theor. Phys. 43 585
[17] ］Song L N，Zhang H Q 2005 Commun. Theor. Phys. 44 783
[18] ］Wadati M J 1975 Phys. Soc. Jpn. 38 673, 681
[19] ］Pego R L，Smereka P，Weinstein MI 1993 Physica D 67 45
[20] ］Dey B. 1986 J. Phys. A 19 19
[21] ］Coffey M W，SIAM J 1990 Appl. Math. 50 1580
[22] ］Zhang W G，Chang Q S，Jiang B G 2002 Chaos Solitons and Fractals 13 311
[23] ］Liu S K，Fu Z T，Liu S D，Zhao Q 2002 Acta Phys. Sin. 51 1923(in Chinese) ［刘式适、付遵涛、刘式达、赵强 2002 51 1923］
[24] ］Lu D C，Hong B J，Tian L X 2006 Acta Phys. Sin. 55 5617 (in Chinese) ［卢殿臣、烘宝剑、田立新 2006 55 5617］
[25] ］Pan J T，Gong，L X 2007 Acta Phys. Sin. 56 5585 (in Chinese) ［潘军廷、龚伦训 2007 56 5585］
[26] ］Shi Y R，Guo P，Lü K P，Duan W S 2004 Acta Phys. Sin. 53 3265 (in Chinese)［石玉仁、郭 鹏、吕克璞、段文山 2004 53 3265］
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[1] ［1］Ablowitz M J，Clarkson P A 1991 Solitons, nonlinear evolution equations and inverse scattering (New York: Cambridge University Press)
[2] ［2］Wadati M. J 1972 Phys. Soc. Jpn. 32 1681
[3] ［3］Hirota R 1971 Phys. Rev. Lett. 27 1192
[4] ［4］Lou S Y 2000 Phys. Lett. A 277 94
[5] ［5］Wang M L 1995 Phys. Lett. A 199 169
[6] ［6］Parkes E J，Duffy B R 1996 Comp. Phys. Commun. 98 288 Parkes E J，Duffy B R 1997 Phys. Lett. A 229 217
[7] ［7］Khater A H，Malfliet W， Callebaut D K， Kamel E S 2002 Chaos, Solitons and Fractals 14 513
[8] ［8］Fan E G 2000 Phys. Lett. A 277 212 Fan E G 2001 Phys. Lett. A 282 18
[9] ［9］Elwakil S A，El-labany S K，Zahran M A，Sabry R 2002 Phys.Lett. A 299 179
[10] ］Gao Y T，Tian B 2001 Comp. Phys.Commun. 133 158
[11] ］Wang Q，Chen Y，Zhang H Q 2005 Phys. Lett. A 340 411
[12] ］Wang J，Zhang X L，Song L N，Zhang H Q 2006 Appl.Math. Comput.182 1330
[13] ］Li Z B，Liu Y P 2002 Comp. Phys. Commun. 148 256
[14] ］Yan Z Y，Zhang H Q 1999 Phys. Lett. A 252 291
[15] ］Li B，Chen Y，Zhang H Q 2003 Chaos Solitons and Fractals 15 647
[16] ］Xie F D，Chen J，Lü Z S 2005 Commun. Theor. Phys. 43 585
[17] ］Song L N，Zhang H Q 2005 Commun. Theor. Phys. 44 783
[18] ］Wadati M J 1975 Phys. Soc. Jpn. 38 673, 681
[19] ］Pego R L，Smereka P，Weinstein MI 1993 Physica D 67 45
[20] ］Dey B. 1986 J. Phys. A 19 19
[21] ］Coffey M W，SIAM J 1990 Appl. Math. 50 1580
[22] ］Zhang W G，Chang Q S，Jiang B G 2002 Chaos Solitons and Fractals 13 311
[23] ］Liu S K，Fu Z T，Liu S D，Zhao Q 2002 Acta Phys. Sin. 51 1923(in Chinese) ［刘式适、付遵涛、刘式达、赵强 2002 51 1923］
[24] ］Lu D C，Hong B J，Tian L X 2006 Acta Phys. Sin. 55 5617 (in Chinese) ［卢殿臣、烘宝剑、田立新 2006 55 5617］
[25] ］Pan J T，Gong，L X 2007 Acta Phys. Sin. 56 5585 (in Chinese) ［潘军廷、龚伦训 2007 56 5585］
[26] ］Shi Y R，Guo P，Lü K P，Duan W S 2004 Acta Phys. Sin. 53 3265 (in Chinese)［石玉仁、郭 鹏、吕克璞、段文山 2004 53 3265］
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