Exact Group Invariant Solutions and Conservation Laws of the Complex Modified Korteweg–de Vries Equation
Exact Group Invariant Solutions and Conservation Laws of the Complex Modified Korteweg–de Vries Equation
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DOI：
10.5560/zna.2013-0027
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发表时间：
2013-09
期刊：
影响因子：
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通讯作者：
A. G. Johnpillai;A. Kara;A. Biswas
中科院分区：
文献类型：
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作者：
A. G. Johnpillai;A. Kara;A. Biswas
从Lie对称性的角度出发，通过分析偏微分方程组，研究标量复修正Korteweg-de弗里斯（cmKdV）方程.这些系统的偏微分方程得到的基本cmKdV方程分解成真实的和虚部。我们导出了偏微分方程组的李点对称生成元，并对它们进行了分类，得到了偏微分方程组的李对称代数的一维子代数的最优系统。这些子代数，然后用来构造一些对称性的减少和精确的群不变的解决方案，系统的偏微分方程。最后，利用李对称方法，构造了几个新的守恒律。随后，根据它们各自的守恒密度计算各自的守恒量。
We study the scalar complex modified Korteweg-de Vries (cmKdV) equation by analyzing a system of partial differential equations (PDEs) from the Lie symmetry point of view. These systems of PDEs are obtained by decomposing the underlying cmKdV equation into real and imaginary components. We derive the Lie point symmetry generators of the system of PDEs and classify them to get the optimal system of one-dimensional subalgebras of the Lie symmetry algebra of the system of PDEs. These subalgebras are then used to construct a number of symmetry reductions and exact group invariant solutions to the system of PDEs. Finally, using the Lie symmetry approach, a couple of new conservation laws are constructed. Subsequently, respective conserved quantities from their respective conserved densities are computed.