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基于Bell多项式,构造了获得非线性发展方程双线性形式的一个新算法,并且开发了相应的程序包.非线性发展方程与其双线性形式之间的变换可由该程序包自动推导,同时给出了一些具有代表性的实例验证了该程序包的有效性与可靠性. 相似文献
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The prolongation structure methodologies of Wahlquist--Estabrook [Wahlquist H D and Estabrook F B 1975 J. Math. Phys. 16 1] for nonlinear differential equations are applied to a variable-coefficient KdV equation. Based on the obtained prolongation structure, a Lie algebra with five parameters is constructed. Under certain conditions, a Lie algebra representation and three kinds of Lax pairs for the variable- coefficient KdV equation are derived. 相似文献
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Based on the invariant expansion method,some reasonable approximate solutions of coupled Korteweg-de Vries(KdV)equations with diferent linear dispersion relations have been obtained.These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacobi elliptic functions.The results also show that if the arbitrary constants are selected suitably,the approximate solutions may become the exact ones. 相似文献
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Higher-order localized waves in coupled nonlinear Schr6dinger equations are investigated by the generalized Darboux transformation. We show that two dark-bright solitons together with a second-order rogue wave of fundamental or triangular pattern and two breathers together with a second-order rogue wave of fundamentM or triangular pattern coexist in the second-order localized wave for the coupled system. Moreover, by increasing the value of one free parameter, the nonlinear waves in the second-order localized wave can merge with each other. The results further reveal the abundant dynamic behaviors of localized waves in coupled systems. 相似文献
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A fractional-order generalized Lorenz system is constructed and numerically investigated. Chaotic behavior existing in the fractional-order generalized Lorenz system is found. The numerical simulations and interesting figures are performed. 相似文献
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Riccati-type Bcklund transformations of nonisospectral and generalized variable-coefficient KdV equations 下载免费PDF全文
We extend the method of constructing Bcklund transformations for integrable equations through Riccati equations to the nonisospectral and the variable-coefficient equations. By taking nonisospectral and generalized variable-coefficient Korteweg–de Vries(KdV) equations as examples, their B¨acklund transformations are obtained under a more generalized constrain condition. In addition, the Lax pairs and infinite numbers of conservation laws of these equations are given. Especially, some classical equations such as the cylindrical KdV equation are just the special cases of the constrain condition. 相似文献
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Based on the invariant expansion method, some reasonable approximate solutions of coupled Korteweg-de Vries (KdV) equations with different linear dispersion relations have been obtained. These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacob/elliptic functions. The results also show that if the arbitrary constants are selected suitably, the approximate solutions may become the exact ones. 相似文献