Solitary wave solutions for a generalized KdV-mKdV equation with variable coefficients
Solitary wave solutions for a generalized KdV-mKdV equation with variable coefficients
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DOI：
10.1016/j.matcom.2010.02.001
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发表时间：
2010-05
期刊：
影响因子：
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通讯作者：
H. Triki;T. Taha;A. Wazwaz
中科院分区：
文献类型：
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作者：
H. Triki;T. Taha;A. Wazwaz
本文研究了等离子体物理和海洋动力学中的广义变系数KdV-mKdV（Gardner）方程。通过对Wazwaz在2007年提出的三种振幅估计进行修正，得到了该模型的钟型孤立波、扭型孤立波和组合型孤立波解.更重要的是，在证明了非线性薛定谔方程组的组合孤波解的存在性之后，结果表明非齐次KdV型方程组存在组合孤波解。值得注意的是，所获得的孤立波解的特征是用时间相关系数表示的。此外，我们给出了所考虑的变系数KdV-mKdV方程的解的形成条件。
In this work, a generalized time-dependent variable coefficients combined KdV–mKdV (Gardner) equation arising in plasma physics and ocean dynamics is studied. By means of three amplitude ansatz that possess modified forms to those proposed by Wazwaz in 2007, we have obtained the bell type solitary waves, kink type solitary waves, and combined type solitary waves solutions for the considered model. Importantly, the results show that there exist combined solitary wave solutions in inhomogeneous KdV-typed systems, after proving their existence in the nonlinear Schrödinger systems. It should be noted that, the characteristics of the obtained solitary wave solutions have been expressed in terms of the time-dependent coefficients. Moreover, we give the formation conditions of the obtained solutions for the considered KdV–mKdV equation with variable coefficients.