共查询到19条相似文献,搜索用时 93 毫秒
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利用改进的G’/G展开方法,借助于计算机代数系统Mathematica成功获得了一大类非线性波动方程一系列新的含有多个参数的精确行波解.这些解包括孤立波解、双曲函数解、三角函数解. 相似文献
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修正的BBM方程的一些新的精确解 总被引:4,自引:0,他引:4
龚伦训 《原子与分子物理学报》2006,23(4):725-728
用修正影射法解修正的BBM(mBBM)方程,得到了一些新的精确解.这个方法的优点在于:①待定函数f(ξ)的指数i的范围从N扩大到-N;②可以不必给出函数f(ξ)的具体表达式求解方程,这样便于寻找更多的解.本文就是利用了这一特点,选择合适的参数,得到一些mBBM方程新的精确解.我们相信;这个方法还可以推广到含有更多维和更高阶的求导项的方程. 相似文献
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An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics. 相似文献
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New explicit exact solutions for a generalized Hirota—Satsuma coupled KdV system and a coupled MKdV equation 总被引:7,自引:0,他引:7 下载免费PDF全文
In this paper,we make use of a new generalized ansatz in the homogeneous balance method,the well-known Riccati equation and the symbolic computation to study a generalized hirota-Satsuma coupled KdsV system and a coupled MKdv equation,respectively,As a result,numerous explicit exact solutions,comprising new solitary wave solutions,periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions,are obtained. 相似文献
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Using the tanh method and a variable separated ordinary difference equation method to solve the double sineGordon equation, we derive some new exact travelling wave solutions, especially a new type of noncontinuous solitary wave solutions. These noncontinuous solitary wave solutions are verified by using the conservation law theory. 相似文献
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含高阶非线性效应的薛定谔方程的精确解研究 总被引:1,自引:0,他引:1
利用孤子理论,研究了含三次和五次非线性项的非线性薛定谔方程,在参数取不同值时得到了方程的新型亮孤子解、新型暗孤子解和新的三角函数周期解。 相似文献
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《Physics letters. A》2006,353(1):40-47
The extended Jacobi elliptic function expansion methods with a computerized symbolic computation are used to construct the exact periodic solutions of some polynomials or nonlinear evolution equations. As a result, many exact travelling wave solutions are obtained which include new solitary or shock wave solution and envelope solitary and shock wave solutions. 相似文献
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In the study of many problems of mechanical and physical sciences, various versions of the Benjamin-Bona-Mahony (BBM) equation
or the regularized-long-wave equation have been proposed. In this paper, we obtain the solitary-wave solutions to the general
form of the BBM equation, which fully cover the variety of the BBM solitary waves previously reported.
This work has been supported by the China Talent Fund, by the Cheung Kong Scholars Programme of China, by the Cheung-Kong-Scholar
Research Concerted Fund of Beijing University of Aeronautics and Astronautics, and by the Doctoral Education Fund in Basic
Sciences of Beijing University of Aeronautics and Astronautics. 相似文献
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ZHENG Chun-Long FEI Jin-Xi 《理论物理通讯》2007,48(4):657-661
Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions (including solltary wave solutlons, periodic wave solutions and rational function solutions) with arbitrary functions [or the (2+ 1)-dimensional general/zed Broer-Kaup (GBK) system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the (2+1)-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed. 相似文献
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In terms of the solutions of an auxiliary ordinary differential
equation, a new algebraic method, which contains the terms of first-order
derivative of functions f(ξ), is constructed to explore the new solitary wave solutions for nonlinear evolution equations. The method is applied to a compound KdV-Burgers equation, and abundant new solitary wave solutions are obtained. The algorithm is also applicable to a large variety of nonlinear evolution equations. 相似文献
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By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献