Solutions and Painleve Property for the KdV Equation with Self-Consistent Source

Shen Yali; Yao Ruoxia

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Solutions and Painleve Property for the KdV Equation with Self-Consistent Source

机译：具有自洽源的KdV方程的解和Painleve性质

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In this paper, the polynomial solutions in terms of Jacobi's elliptic functions of the KdV equation with a self-consistent source (KdV-SCS) are presented. The extended (G'/G)-expansion method is utilized to obtain exact traveling wave solutions of the KdV-SCS, which finally are expressed in terms of the hyperbolic function, the trigonometric function, and the rational function. Meanwhile we find the Lie point symmetry and Lie symmetry group and give several group-invariant solutions for the KdV-SCS. Finally, we supplement the results of the Painleve property in our previous work and get the Backlund transformations of the KdV-SCS.

机译：本文提出了具有自洽源（KdV-SCS）的KdV方程的Jacobi椭圆函数的多项式解。利用扩展的（G'/ G）扩展方法获得KdV-SCS的精确行波解，该解最终以双曲函数，三角函数和有理函数表示。同时我们找到了Lie点对称性和Lie对称性组，并给出了KdV-SCS的几个组不变解。最后，我们在先前的工作中补充了Painleve属性的结果，并获得了KdV-SCS的Backlund变换。

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《Mathematical Problems in Engineering》 |2018年第15期|4014382.1-4014382.16|共16页
作者
Shen Yali; Yao Ruoxia;
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Shaanxi Normal Univ Sch Comp Sci Xian 710119 Shaanxi Peoples R China|Yuncheng Univ Dept Appl Math Yuncheng 044000 Shanxi Peoples R China;

Shaanxi Normal Univ Sch Comp Sci Xian 710119 Shaanxi Peoples R China;

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1. Solutions and Painlevé Property for the KdV Equation with Self-Consistent Source [J] . Yali Shen, Ruoxia Yao Mathematical Problems in Engineering: Theory, Methods and Applications . 2018,第5期

机译：具有自洽源的KdV方程的解和Painlevé性质
2. Negaton, positon and complexiton solutions of the nonisospectral KdV equations with self-consistent sources [J] . Jun Su, Wei Xu, Genjiu Xu, Communications in Nonlinear Science and Numerical Simulation . 2012,第1期

机译：具有自洽源的非等谱KdV方程的Negaton，位置和复杂性解
3. Positon solutions of the KdV equation with self-consistent sources [J] . Y. B. Zeng, Y. J. Shao, W. M. Xue Theoretical and mathematical physics . 2003,第2期

机译：具有自洽源的KdV方程的正解
4. Generalized Kaup—Kupershmidt Solitons, Static Solitons andBoundary Generated Solitons — Solutions of the KdV andHigher Order KdV Equations [C] . G.I. Burde International Conference on Numerical Analysis and Applied Mathematics . 2010

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7. On Discrete Painleve Equations Associated with the Lattice KdV Systems and the Painleve VI Equation [O] . Nijhoff, F. W., Ramani, A., Grammaticos, B., 1998

机译：关于与格子KdV系统相关的离散painleve方程和painleve VI方程
8. Method of Solution for Painleve Equations: Painleve IV, V [R] . Fokas, A. S., Mugan, U., Ablowitz, M. J. 1987

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Solutions and Painleve Property for the KdV Equation with Self-Consistent Source

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