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Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation 下载免费PDF全文
This paper is concerned with the generalized variable-coefficient nonlinear evolution equation(vc-NLEE).The complete integrability classification is presented,and the integrable conditions for the generalized variable-coefficient equations are obtained by the Painlev′e analysis.Then,the exact explicit solutions to these vc-NLEEs are investigated by the truncated expansion method,and the Lax pairs(LP) of the vc-NLEEs are constructed in terms of the integrable conditions. 相似文献
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运用经典李群方法研究了正则长波-KdV方程,得到所有的向量场.然后,将正则长波-KdV方程约化成常微分方程,进一步利用e-φ(ε))展开法和Lambert W函数法求精确解.最后,利用李点对称求正则长波-KdV方程的伴随方程和守恒律. 相似文献
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In this paper, the Lie group classification method is performed on the fractional partial differential equation(FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations(FODEs) in terms of the Erd′elyi-Kober(E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs. 相似文献
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