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利用扩展的Sinh—Gordon方程展开法研究了Kaup—Kupershmidt方程的Jacobi椭圆函数解,此方法也适用于求解其他非线性演化方程,从而丰富了方程解的范围. 相似文献
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LIU Cheng-Shi 《理论物理通讯》2008,49(1):153-158
Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Gordon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method are not true. Finally, we prove that our solutions to sinh-Gordon equation include all solutions obtained in the paper [Z.T. Fu, et al., Commun. Theor. Phys. (Beijing, China) 45 (2006) 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions. 相似文献
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弱色散非线性波动方程的孤波解和Jacobi椭圆函数解 总被引:2,自引:2,他引:0
应用影射法解传输线中弱色散非线性波动方程,得到了孤波解和Jacobi椭圆函数解,并用Matlab绘图加以说明. 相似文献
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In this paper, dependent and independent variable transformations are introduced to solve the negative mKdV equation systematically by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different kinds of solutions can be obtained to the negative mKdV equation, including breather lattice solution and periodic wave solution. 相似文献
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(2+1)维色散长波方程的扩展椭圆函数有理展开解法 总被引:2,自引:0,他引:2
在一个新的更一般的假设下,借助于符号计算,提出了一个椭圆函数有理展开法,并用它统一地求出许多非线性发展方程新的双周期精确解.本文选择(2+1)维色散长波方程作为此方法的应用来加以说明.得到了Yan方法所得的所有解,并且得到更多的一般形式的解.在m取它的极限时,可得到许多冲击波解和孤立波解. 相似文献
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利用Jacobi椭圆函数得到了自由端受集中载荷悬臂梁大挠度弯曲问题的显式精确解,不同于由传统椭圆积分公式得到的解,该显式精确解给出梁中任意点的转角,由此可方便的得到梁弯曲后各点的位移.研究表明:由该解出发,可得到任意位置受集中载荷悬臂梁问题的解;对称性分析表明该解可直接用于两端简支或两端固支梁中点受集中载荷的情况.最后分别给出了载荷取一系列值时以上三种边界条件下梁弯曲的挠度曲线. 相似文献
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ZHANG Huan TIAN Bo ZHANG Hai-Qiang LI Li-Li 《理论物理通讯》2009,51(4):588-594
The present work extends the search of Jacobi elliptic function solutions for the multi-component modified Korteweg-de Vries equations. When the modulum m →1, those periodic solutions degenerate as the corresponding solitary wave and shock wave ones. Especially, exact solutions for the three-component system are presented in detail and graphically. 相似文献