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1.
非线性耦合标量场方程的新双周期解(Ⅱ)   总被引:3,自引:0,他引:3       下载免费PDF全文
李德生  张鸿庆 《物理学报》2003,52(10):2379-2385
基于具有双周期解的常微分方程,提出了一种构造非线性微分方程双周期解的新方法,在计算机符号软件帮助下方法可实现机械化.应用此方法于非线性耦合标量场方程,得到了该方程的大量的新精确解. 关键词: 非线性耦合标量场方程 双周期解 精确解  相似文献   

2.
非线性发展方程的丰富的Jacobi椭圆函数解   总被引:6,自引:0,他引:6       下载免费PDF全文
吕大昭 《物理学报》2005,54(10):4501-4505
通过把十二个Jacobi椭圆函数分类成四组,提出了新的广泛的Jacobi椭圆函数展开法,利用这一方法求得了非线性发展方程的丰富的Jacobi椭圆函数双周期解.当模数m→0或1时,这些解退化为相应的三角函数解或孤立波解和冲击波解. 关键词: 非线性发展方程 Jacobi椭圆函数 双周期解 行波解  相似文献   

3.
非线性耦合标量场方程的精确解   总被引:9,自引:2,他引:7       下载免费PDF全文
范恩贵  张鸿庆  林钢 《物理学报》1998,47(7):1064-1070
在非线性耦合标量场方程已有精确解基础上,利用适当的函数变换方法,再次获得几种精确解,从而新旧结果一起构成耦合标量场方程的8种精确解,其中有6种孤子解,另外两种为三角函数形式的周期解.讨论了这些结果在物理学其他几个著名方程上的应用. 关键词:  相似文献   

4.
将文[22]中提出的求解非线性演化方程的Weierstrass椭圆函数解的一个新方法应用于Time Dependent Ginzburg-Landau方程,获得了该方程的一些新的双周期解,并在退化情形下得到了一些新的精确孤波解.  相似文献   

5.
一类新的复合场方程及解   总被引:2,自引:0,他引:2       下载免费PDF全文
王永久  唐智明 《物理学报》2000,49(4):597-601
采用5维空间4+1分解的方法建立了标量场、电磁场和引力场的复合场方程,并给出了一个复合场方程的静态球对称解 当标量场及其与电磁场的耦合不存在时(β=0),此解退化为ReissnerNordtstrom度规.还给出了标量场和电磁场产生的复合场源流密度矢量的表示式 关键词:  相似文献   

6.
(2+1) 维Broer-Kau-Kupershmidt方程一系列新的精确解   总被引:3,自引:0,他引:3       下载免费PDF全文
智红燕  王琪  张鸿庆 《物理学报》2005,54(3):1002-1008
借助于符号计算软件Maple,通过一种构造非线性偏微分方程(组)更一般形式精确解的直接方法即改进的代数方法,求解(2+1) 维 Broer-Kau-Kupershmidt方程,得到该方程的一系列新的精确解,包括多项式解、指数解、有理解、三角函数解、双曲函数解、Jacobi 和 Weierstrass 椭圆函数双周期解. 关键词: 代数方法 (2+1) 维 Broer-Kau-Kupershmidt 方程 精确解 行波解  相似文献   

7.
套格图桑 《物理学报》2011,60(7):70203-070203
为了获得sine-Gordon型方程的无穷序列精确解,给出三角函数型辅助方程和双曲函数型辅助方程及其Bäcklund变换和解的非线性叠加公式,借助符号计算系统Mathematica,构造了sine-Gordon方程、mKdV-sine-Gordon方程、(n+1)维双sine-Gordon方程和sinh-Gordon方程的无穷序列新精确解.其中包括无穷序列三角函数解、无穷序列双曲函数解、无穷序列Jacobi椭圆函数解和无穷序列复合型解. 关键词: sine-Gordon型方程 解的非线性叠加公式 辅助方程 无穷序列精确解  相似文献   

8.
Jacobi 椭圆函数展开法的新应用   总被引:31,自引:4,他引:27       下载免费PDF全文
张善卿  李志斌 《物理学报》2003,52(5):1066-1070
通过引入“秩”的概念, 对非线性发展方程进行分类, 将Jacobi椭圆函数展开法推广应用到一类新的非线性发展方程, 并给出了它们的精确周期解. 关键词: 非线性发展方程 周期解 孤立波解 Jacobi椭圆函数  相似文献   

9.
套格图桑 《物理学报》2011,60(5):50201-050201
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   

10.
非线性Schroedinger方程的包络形式解   总被引:4,自引:0,他引:4       下载免费PDF全文
扩展了最近提出的F展开方法以构造非线性演化方程更多的精确解,即将F展开法中的一阶非线性常微分方程和单变量的有限幂级数代之以类似的一阶常微分方程组和两个变量的有限幂级数,这两个变量是一阶常微分方程组的解分量.作为例子,用扩展的F展开法解非线性Schroedinger方程,得到了很丰富的包络形式的精确解,特别是以两个不同的Jacobi椭圆函数表示的解.显然,扩展的F展开方法也可以解其他类型的非线性演化方程.  相似文献   

11.
Many physical systems can be successfully modelled using equations that admit the soliton solutions. In addition, equations with soliton solutions have a significant mathematical structure. In this paper, we study and analyze a three-dimensional soliton equation, which has applications in plasma physics and other nonlinear sciences such as fluid mechanics, atomic physics, biophysics, nonlinear optics, classical and quantum fields theories. Indeed, solitons and solitary waves have been observed in numerous situations and often dominate long-time behaviour. We perform symmetry reductions of the equation via the use of Lie group theory and then obtain analytic solutions through this technique for the very first time. Direct integration of the resulting ordinary differential equation is done which gives new analytic travelling wave solutions that consist of rational function, elliptic functions, elementary trigonometric and hyperbolic functions solutions of the equation. Besides, various solitonic solutions are secured with the use of a polynomial complete discriminant system and elementary integral technique. These solutions comprise dark soliton, doubly-periodic soliton, trigonometric soliton, explosive/blowup and singular solitons. We further exhibit the dynamics of the solutions with pictorial representations and discuss them. In conclusion, we contemplate conserved quantities for the equation under study via the standard multiplier approach in conjunction with the homotopy integral formula. We state here categorically and emphatically that all results found in this study as far as we know have not been earlier obtained and so are new.  相似文献   

12.
(2+1)维色散长波方程的新的类孤子解   总被引:14,自引:0,他引:14       下载免费PDF全文
曾昕  张鸿庆 《物理学报》2005,54(2):504-510
应用一种新的修改的代数方法去求解(2+1)维色散长波方程,获得方程的大量新的精确解.这些解包括类孤子解、类周期解、类有理解、类双曲函数解、类Jacobi椭圆函数解等等. 关键词: (2+1)维色散长波方程 类孤子解 类有理解 类双曲函数解 类Jacobi椭圆 函数解  相似文献   

13.
《中国物理 B》2021,30(6):60202-060202
The nonlinear Schro¨dinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas.However,due to the difficulty of solving this equation,in particular in high dimensions,lots of methods are proposed to effectively obtain different kinds of solutions,such as neural networks among others.Recently,a method where some underlying physical laws are embeded into a conventional neural network is proposed to uncover the equation’s dynamical behaviors from spatiotemporal data directly.Compared with traditional neural networks,this method can obtain remarkably accurate solution with extraordinarily less data.Meanwhile,this method also provides a better physical explanation and generalization.In this paper,based on the above method,we present an improved deep learning method to recover the soliton solutions,breather solution,and rogue wave solutions of the nonlinear Schro¨dinger equation.In particular,the dynamical behaviors and error analysis about the one-order and two-order rogue waves of nonlinear integrable equations are revealed by the deep neural network with physical constraints for the first time.Moreover,the effects of different numbers of initial points sampled,collocation points sampled,network layers,neurons per hidden layer on the one-order rogue wave dynamics of this equation have been considered with the help of the control variable way under the same initial and boundary conditions.Numerical experiments show that the dynamical behaviors of soliton solutions,breather solution,and rogue wave solutions of the integrable nonlinear Schro¨dinger equation can be well reconstructed by utilizing this physically-constrained deep learning method.  相似文献   

14.
In this paper, based on new auxiliary nonlinear ordinary differential equation with a sixth-degree nonlinear term, we study the (2 1)-dimensional Davey-Stewartson equation and new types of travelling wave solutions are obtained, which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions, and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations.  相似文献   

15.
By using the extended homogeneous balance method, a new auto-Backlund transformation(BT) to thegeneralized Kadomtsev-Petviashvili equation with variable coefficients (VCGKP) are obtained. And making use of theauto-BT and choosing a special seed solution, we get many families of new exact solutions of the VCGKP equations,which include single soliton-like solutions, multi-soliton-like solutions, and special-soliton-like solutions. Since the KPequation and cylindrical KP equation are all special cases of the VCGKP equation, and the corresponding results ofthese equations are also given respectively.  相似文献   

16.
In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized (m, 2Nm)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations.  相似文献   

17.
With the aid of the symbolic computation, we improve Xie's algorithm [F. Xie, Z.Y. Yan, H. Zhang, Phys. Lett. A 285 (2001) 76], and present a new extended method. Based on the new general ansatz (3), we successfully solve a compound KdV-MKdV equation, and obtain some special solutions which contain soliton solutions, and periodic solutions. The method can also be applied to other nonlinear partial differential equations.  相似文献   

18.
In this Letter, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. In order to illustrate the validity and the advantages of the method we choose the Ostrovsky equation. As a result, many new and more general exact solutions have been obtained for the equation.  相似文献   

19.
In this paper we present the full classification of symmetry-invariant solutions for the Gibbons–Tsarev equation. Then we use these solutions to construct explicit expressions for two-component reductions of Benney’s moments equations, to get solutions of Pavlov’s equation, and to find integrable reductions of the Ferapontov–Huard–Zhang system, which describes implicit two-phase solutions of the dKP equation.  相似文献   

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