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利用修正的Clarkson-Kruskal 直接法对变系数Whitham-Broer-Kaup（VCWBK）方程组进行等价转化，建立了VCWBK 方程组与常系数WBK 方程组解之间的关系，并得到了常系数WBK 方程组的一些对称和相似约化. 借助辅助函数法得到了VCWBK 方程组的一些新精确解，包括有理函数解、双曲函数的解、三角函数解和Jacobi 椭圆函数解.
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关键词:
- 变系数Whitham-Broer-Kau方程组 /
- 修正的Clarkson-Kruskal直接法 /
- 相似约化 /
- 精确解
An equivalence transformation of Whitham-Broer-Kaup equations with variable coefficients (VCWBK) is obtainedby using modified Clarkson-Kruskal direct method. Further, the relationship between the solutions of VCWBK equationsand ones of the corresponding WBK equations with constant coefficients is obtained. In addition, by applying directsymmetry method, some symmetries and similarity reductions of the corresponding WBK equations with constantcoefficients are derived. Using an auxiliary function to solve some special cases, we obtain some new exact solutionsof VCWBK equations, including rational solutions, hyperbolic function solutions, trigonometric function solutions, andJacobi elliptic function solutions.-
Keywords:
- Whitham-Broer-Kaup equations with variable coefficients /
- modified Clarkson-Kruska direct method /
- similarity reductions /
- exact solutions
[1] Yu Y D, Ma H C 2010 Appl. Math. Comput. 215 3534
[2] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese) [范恩贵, 张鸿庆1998 47 353]
[3] Dong Z Z, Chen Y, Lang H Y 2010 Chin. Phys. B 19 090205
[4] Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 1569 (in Chinese) [李德生, 张鸿庆2003 52 1569]
[5] Chen Y M, Ma S H, Ma Z Y 2013 Chin. Phys. B 22 050510
[6] Bekir A, Ayhan B, Özer M N 2013 Chin. Phys. B 22 010202
[7] Clarkson P A, Kruskal M D 1989 J. Math. Phys. 30 2201
[8] Lou S Y 1990 Phys. Lett. A 151 133
[9] Yan Z L, Zhou J P 2010 Commun. Theor. Phys. 54 965
[10] Yan Z L, Liu X Q 2005 Commun. Theor. Phys. 44 479
[11] Zhang Z Y, Yong X L, Chen Y F 2008 J. Nonlinear Math. Phys. 15 383
[12] Emmanuel Y, Peng y Z 2006 Acta. J. Theor. Phys. 45 197
[13] Yan Z Y, Zhang H Q 2001 Phys. Lett. A 285 355
[14] Mohammed Khalfallah 2009 Math. Comput. Model. 49 666
[15] Tian Y H, Chen H L, Liu X Q 2010 Appl. Math. Comput. 215 3509
[16] Zhang L H, Liu X Q, Bai C L 2007 Commun. Theor. Phys. (Beijing, China) 48 405
[17] Bai C L, Bai C J, Zhao H 2005 Z. Naturforsch. 60a 211
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[1] Yu Y D, Ma H C 2010 Appl. Math. Comput. 215 3534
[2] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese) [范恩贵, 张鸿庆1998 47 353]
[3] Dong Z Z, Chen Y, Lang H Y 2010 Chin. Phys. B 19 090205
[4] Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 1569 (in Chinese) [李德生, 张鸿庆2003 52 1569]
[5] Chen Y M, Ma S H, Ma Z Y 2013 Chin. Phys. B 22 050510
[6] Bekir A, Ayhan B, Özer M N 2013 Chin. Phys. B 22 010202
[7] Clarkson P A, Kruskal M D 1989 J. Math. Phys. 30 2201
[8] Lou S Y 1990 Phys. Lett. A 151 133
[9] Yan Z L, Zhou J P 2010 Commun. Theor. Phys. 54 965
[10] Yan Z L, Liu X Q 2005 Commun. Theor. Phys. 44 479
[11] Zhang Z Y, Yong X L, Chen Y F 2008 J. Nonlinear Math. Phys. 15 383
[12] Emmanuel Y, Peng y Z 2006 Acta. J. Theor. Phys. 45 197
[13] Yan Z Y, Zhang H Q 2001 Phys. Lett. A 285 355
[14] Mohammed Khalfallah 2009 Math. Comput. Model. 49 666
[15] Tian Y H, Chen H L, Liu X Q 2010 Appl. Math. Comput. 215 3509
[16] Zhang L H, Liu X Q, Bai C L 2007 Commun. Theor. Phys. (Beijing, China) 48 405
[17] Bai C L, Bai C J, Zhao H 2005 Z. Naturforsch. 60a 211
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