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WANG Ming-Liang LI Er-Qiang LI Xiang-Zheng 《理论物理通讯》2007,47(1):1-9
The purpose of the present paper is twofold. First, the projective Riccati equations (PREs for short) are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values of coeffcients of PREs, the solutions with two arbitrary parameters of PREs can be expressed by the hyperbolic functions, the trigonometric functions, and the rational functions respectively, at the same time the relation between the components of each solution to PREs is also implemented. Second, more new travelling wave solutions for some nonlinear PDEs, such as the Burgers equation, the mKdV equation, the NLS^+ equation, new Hamilton amplitude equation, and so on, are obtained by using Sub-ODE method, in which PREs are taken as the Sub-ODEs. The key idea of this method is that the travelling wave solutions of nonlinear PDE can be expressed by a polynomial in two variables, which are the components of each solution to PREs, provided that the homogeneous balance between the higher order derivatives and nonlinear terms in the equation is considered. 相似文献
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Maha S. M. Shehata Hadi Rezazadeh Emad H. M. Zahran Eric Tala-Tebue Ahmet Bekir 《理论物理通讯》2019,71(11):1275-1280
In this article, we employ the perturbed Fokas-Lenells equation(FLE), which represents recent electronic communications. The Riccati-Bernoulli Sub-ODE method which does not depend on the balance rule is used for thefirst time to obtain the new exact and solitary wave solutions of this equation. This technique is direct, effective and reduces the large volume of calculations. 相似文献
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Houria Triki 《Applied mathematics and computation》2009,214(2):370-373
In this work, an auxiliary equation is used for an analytic study on the time-variable coefficient modified Korteweg-de Vries (mKdV) equation. Five sets of new exact soliton-like solutions are obtained. The results show that the pulse parameters are time-dependent variable coefficients. Moreover, the basic conditions for the formation of derived solutions are presented. 相似文献
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In this paper, a method with the aid of a sub-ODE and its solutions is used for constructing new periodic wave solutions for nonlinear Gardner equation and BBM equation with nonlinear terms of any order arising in mathematical physics. As a result, many exact traveling wave solutions are successfully obtained. The method in the paper is very direct and it can also be applied to other nonlinear evolution equations. 相似文献
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