共查询到20条相似文献,搜索用时 140 毫秒
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本文为了获得非线性发展方程新的无穷序列精确解,给出了几种辅助方程的Böcklund变换和解的非线性叠加公式,并构造了一些非线性发展方程新的无穷序列精确解,其中包括无穷序列Jacobi椭圆函数解、无穷序列双曲函数解和无穷序列三角函数解.该方法在构造非线性发展方程无穷序列精确解方面具有普遍意义.
关键词:
辅助方程法
解的非线性叠加公式
无穷序列解
非线性发展方程 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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用修正的影射法解非线性薛定谔方程,得到了一些新的Jacobi椭圆函数展开解.
关键词:
Jacobi椭圆函数
非线性薛定谔方程
修正影射法
行波解 相似文献
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The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations. 相似文献
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The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations. 相似文献
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In this paper, the new exact solutions for some nonlinear partial differential equations are obtained within the newly established conformable derivative. We use the first integral method to establish the exact solutions for time-fractional Burgers’ equation, modified Burgers’ equation, and Burgers–Korteweg–de Vries equation. We report that this method is efficient and it can be successfully used to obtain new analytical solutions of nonlinear FDEs. 相似文献
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Using the extension homogeneous balance method,we have obtained some new special types of soliton solutions of the (2+1)-dimensional KdV equation.Starting from the homogeneous balance method,one can obtain a nonlinear transformation to simple (2+1)-dimensional KdV equation into a linear partial differential equation and two bilinear partial differential equations.Usually,one can obtain only a kind of soliton-like solutions.In this letter,we find further some special types of the multisoliton solutions from the linear and bilinear partial differential equations. 相似文献
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ZHANG Jie-Fang HUANG Wen-Hua 《理论物理通讯》2001,(11)
Using the extension homogeneous balance method,we have obtained some new special types of soliton solutions of the (2 1)-dimensional KdV equation.Starting from the homogeneous balance method,one can obtain a nonlinear transformation to simple (2 1)-dimensional KdV equation into a linear partial differential equation and two bilinear partial differential equations.Usually,one can obtain only a kind of soliton-like solutions.In this letter,we find further some special types of the multisoliton solutions from the linear and bilinear partial differential equations.`` 相似文献
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In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the (2+1)-dimensional Kaup-Kupershmidt (KK) equation are presented. We successfully obtain more general exact travelling wave solutions for (2+1)-dimensional KK equation by the symmetry method and the (G, /G)-expansion method. Consequently, we find some new solutions of (2+1)-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions. 相似文献
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By means of symbolic computation, a new application of Riccati equation is presented to obtain novel exact solutions of some nonlinear evolution equations, such as nonlinear Klein-Gordon equation, generalized Pochhammer-Chree equation and nonlinear Schrödinger equation. Comparing with the existing tanh methods and the proposed modifications, we obtain the exact solutions in the form as a non-integer power polynomial of tanh (or tan) functions by using this method, and the availability of symbolic computation is demonstrated. 相似文献
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WU Guo-Jiang HAN Jia-Hua ZHANG Wen-Liang ZHANG Miao WANG Jun-Mao 《理论物理通讯》2007,48(5):815-818
By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for generalized Klein-Cordon equation and Benjamin equation, which cannot be found in previous work. This method also can be used to find new periodic wave solutions of other nonlinear evolution equations. 相似文献
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《Waves in Random and Complex Media》2013,23(1):75-90
In this paper, we seek exact solutions of generalized Zakharov system. We use extended trial equation method to obtain exact solutions of this system. Consequently, we obtain some exact solutions including soliton solutions, rational, Jacobi elliptic and hyperbolic function solutions of this system by using extended trial equation method. 相似文献
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Making use of a new generalized ansatz, we present a new generalized extended F-expansion method for constructing the
exact solutions of nonlinear partial differential equations in a unified way. Applying the generalized method with the aid of Maple, we consider the (2+1)-dimentional breaking soliton
equation. As a result, we successfully obtain some new and more general
solutions including Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions, and so on. As an illustrative sample, the properties of some soliton solutions for the breaking soliton equation are shown by some
figures. Our method can also be applied to other partial differential equations. 相似文献