共查询到19条相似文献,搜索用时 70 毫秒
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通过一个辅助性方程和埃米尔特变换研究广义随机KdV方程的随机雅克比椭圆函数类波解.此外,还通过椭圆函数在模数取极限m→0和m→1的情况,给出方程的随机类孤子解和随机三角函数波解,所得结果丰富了广义随机KdV方程的精确解. 相似文献
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一类带有非均匀项的广义KdV方程的孤波解朱佐农(扬州大学农学院基础部,扬州225O01)-、引言众所周知,KdV方程已被广泛研究[1].从方程(1)的高阶守恒量出发,Lax得到第一族高阶KdV方程,其5阶形式为:从(2)的守恒量出发,Sawada和K... 相似文献
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广义组合KdV-mKdV方程的显式精确解 总被引:1,自引:0,他引:1
Abstract. With the aid of Mathematica and Wu-elimination method,via using a new generalizedansatz and well-known Riccati equation,thirty-two families of explicit and exact solutions forthe generalized combined KdV and mKdV equation are obtained,which contain new solitarywave solutions and periodic wave solutions. This approach can also be applied to other nonlinearevolution equations. 相似文献
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通过利用新的G展开法,并借助Mathematica计算软件,研究了一类五阶非线性波方程的精确解,获得了方程的含有多个任意参数的新的显式行波解,分别为三角函数解、双曲函数解、指数函数解,扩大了该类方程的解的范围. 相似文献
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耦合KdV方程的几个精确解 总被引:2,自引:0,他引:2
张金顺 《应用数学与计算数学学报》1990,4(2):27-30
Darboux变换是求孤子方程的精确解的一种新方法。它借助于孤子方程的Lax对。从方程的平凡解导出新的非平凡解。本文对一个四阶特征值问题找出了Darboux变换,并由此得到耦合KdV方程的孤子解,周期解,极点解等。 相似文献
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In this paper,we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method.Based on the modified homogeneous balance method,several kinds of exact(new)solutions of the generalized KdV equation are obtained. 相似文献
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New exact traveling wave solutions are derived for two coupled nonlinear water wave equations by using a delicate way of rank analysis two-step ansatz method. 相似文献
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二维色散长波方程组的精确解 总被引:2,自引:0,他引:2
利用齐次平衡法给出了二维色散长波方程组的定态解、孤立波解与非孤立波解等几种显式精确解。这个方法也可用来寻找其它非线性发展方程的不同类型的精确解。 相似文献
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讨论了带有热源项的非线性扩散方程.通过一种直接简洁的方法得到了几种精确解.该方法可用于更高阶演化方程的求解问题. 相似文献
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A simple and direct method is described to construct the soliton-like solution for the general KdV equation with external force. Crucial to the method is the assumption that the solution chosen is a special truncated expansion. 相似文献
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A class of second order quasilinear differential equations with singular nonlinearities is considered. The set of all possible solutions defined on a positive half-line [a,∞) is classified into six types according to their aymptotic behavior as t→∞, and sharp conditions are established for the existence of solutions belonging to each of the classified types. 相似文献
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Abdul‐Majid Wazwaz 《Numerical Methods for Partial Differential Equations》2007,23(2):247-255
In this work, the sine‐cosine method, the tanh method, and specific schemes that involve hyperbolic functions are used to study solitons and periodic solutions governed by the generalized KdV equation. New solutions are determined by using the hyperbolic functions schemes. The study introduces new approaches to handle nonlinear PDEs in the solitary wave theory. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 247–255, 2007 相似文献
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Zaihong Wang 《Proceedings of the American Mathematical Society》2003,131(2):523-531
In this paper, we study the dynamics of the mappings
where is a irrational rotation number. We prove the existence of orbits that go to infinity in the future or in the past by using the well-known Birkhoff Ergodic Theorem. Applying this conclusion, we deal with the unboundedness of solutions of Liénard equations with asymmetric nonlinearities.
where is a irrational rotation number. We prove the existence of orbits that go to infinity in the future or in the past by using the well-known Birkhoff Ergodic Theorem. Applying this conclusion, we deal with the unboundedness of solutions of Liénard equations with asymmetric nonlinearities.