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1.
朱佐农 《物理学报》1992,41(7):1057-1062
本文研究了推广的KdV方程 ut+2μuux+v3x+δu5x=0(μvδ≠0) (1)的精确孤子解,得到了(1)式的一些新的孤波解,对文献[10]的若干结论作了补充与修正。 关键词:  相似文献   

2.
海文华  肖奕 《物理学报》1996,45(4):587-594
对于一个其耗散项可看作微扰的Burgers-KdV(B-KdV)方程ut+uux+βuxxx=εuxx,|ε|?1,考虑一级近似和行波情形,建立一套求通解的直接扰动方法,利用零级方程的单孤子解,获得一级方程的孤子型通解,它包含任意多个不同的孤子解,每个孤子解分别描述一个位于半无限空间的孤子阵列,分析表明,耗散使得“亮孤子”变矮变窄,“暗孤子”变浅变窄. 关键词:  相似文献   

3.
刘慕仁  孔令江 《物理学报》1996,45(3):370-372
如果将格子Boltzmann方程的碰撞项由Fermi型改为Boltzmann型,可大幅度地降低沾滞系数,从而提高了用格子Boltzmann方程模拟流体运动的效率。理论分析与模拟结果精确的一致。 关键词:  相似文献   

4.
杨征  马松华  方建平 《物理学报》2011,60(4):40508-040508
在符号计算软件Maple的帮助下,利用改进的Riccati方程映射法得到了(2+1)维Zakharov-Kuznetsov方程(ZK)的新显式精确解. 根据得到的解,研究了ZK方程的特殊孤子结构. 关键词: 改进的Riccati方程映射法 Zakharov-Kuznetsov方程 精确解 孤子结构  相似文献   

5.
姜先策  徐斌  梁检初  易林 《物理学报》2013,62(11):110205-110205
本文采用自相似方法求解中空圆柱形边界贝塞尔晶格中变系数非线性薛定谔方程, 得到了与数值模拟解一致的解析解, 表明由非衍射贝塞尔光束诱导的光子晶格可支持稳定的自相似孤子簇. 精确解ψmnn+2层, 2m极的多极孤立波, 其形状及大小在传播过程中保持不变. 关键词: 空间光孤子 贝塞尔晶格 边界 自相似  相似文献   

6.
(2+1)维非线性Burgers方程变量分离解和新型孤波结构   总被引:6,自引:0,他引:6       下载免费PDF全文
徐昌智  张解放 《物理学报》2004,53(8):2407-2412
利用变量分离方法,获得了(2+1)维非线性Burgers方程的变量分离解.由于在Bcklund变换和变量分离步骤中引入了作为种子解的任意函数, 因而精确解中含有三个任意函数(其中一个为条件函数),适当地选择任意函数,可以获得多种形状的扭状孤波解、周期性孤子解和格子型孤波解. 关键词: 变量分离解 非线性波方程 (2+1)维  相似文献   

7.
含外力项的广义KdV方程的类孤子解   总被引:6,自引:1,他引:5       下载免费PDF全文
朱佐农 《物理学报》1992,41(10):1561-1566
本文利用广义KP方程的B?cklund变换,获得了含外力项的广义KdV方程ut+6uux+uxxx+6f(t)u=g(t)+x(f′+12f2) (1)的类孤子解。 关键词:  相似文献   

8.
雷军  马松华  方建平 《物理学报》2011,60(5):50302-050302
利用投射方程法和变量分离法,得到(2+1)维破裂孤子方程的新显式精确解. 根据得到的孤立波解,利用 Weierstrassp 函数,构造出多方孤子局域结构. 利用两个混沌系统研究了破裂孤子方程的混沌行为. 关键词: 投射方程法 破裂孤子方程 多方孤子 混沌行为  相似文献   

9.
利用耦合的Riccati方程组构造微分-差分方程精确解   总被引:2,自引:0,他引:2       下载免费PDF全文
杨先林  唐驾时 《物理学报》2008,57(6):3305-3311
通过引入耦合的Riccati方程组得到一个构造非线性微分-差分方程精确解的代数方法.作为实例,将该方法应用到了一般格子方程,相对论的Toda格子方程和(2+1)维Toda格子方程.借助符号计算软件Mathematica,获得了这些方程的扭结型孤波解和复数解.该方法也适合求解其他非线性微分-差分方程的精确解. 关键词: 耦合Riccati方程组 格子方程 相对论的Toda格子方程 (2+1)维Toda格子方程  相似文献   

10.
一个新(2+1)维非线性演化方程的相干孤子结构   总被引:13,自引:0,他引:13       下载免费PDF全文
张解放  黄文华  郑春龙 《物理学报》2002,51(12):2676-2682
用分离变量法研究了新(2+1)维非线性演化方程的相干孤子结构.由于Bcklund变换和变量分离步骤中引入了作为种子解的任意函数,得到了新(2+1)维非线性演化方程丰富的孤子解.合适地选择任意函数,孤子解可以是solitoffs,dromions,dromion格子,呼吸子和瞬子.呼吸子不仅在幅度、形状,各峰间距离,甚至在峰的数目上都进行了呼吸. 关键词: 新(2+1)维非线性演化方程 分离变量法 孤子结构  相似文献   

11.
The two-parameter family of Estevez-Mansfield-Clarkson equations with fully nonlinear dispersion (called E(m,n) equations),(uz^m)zzτ γ(uz^nuτ)z uττ=0 which is a generalized model of the integrable Estevez-Mansfield-Clarkson equation uzzzτ γ(uzuzτ uzzuτ) uττ=0,is presented.Five types of symmetries of the E9m,n) equation are obtained by making use of the direct reduction method.Using these obtained reductions and some simple transformations,we obtain the solitary-like wave solutions of E(1,n) equation.In addition,we also find the compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions,they reemerge with the same coherent shape) of E(3,2) equation and E(m,m-1) for its potentials,say,uz,and compacton-like solutions of E(m,m-1) equations,respectively.Whether there exist compacton-like solutions of the other E(m,n) equation with m≠n 1 is still an open problem.  相似文献   

12.
We have found two types of important exact solutions,compacton solutions,which are solitary waves with the property that after colliding with their own kind,they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction,in the (1 1)D,(1 2)D and even (1 3)D models,and dromion solutions (exponentially decaying solutions in all direction) in many (1 2)D and (1 3)D models.In this paper,symmetry reductions in (1 2)D are considered for the break soliton-type equation with fully nonlinear dispersion (called BS(m,n) equation)ut b(u^m)xxy 4b(u^n δx^-1uy)x=0,which is a generalized model of (1 2)D break soliton equation ut buxxy 4buuy 4buxδx^-1uy=0,by using the extended direct reduction method.As a result,six types of symmetry reductions are obtained.Starting from the reduction equations and some simple transformations,we obtain the solitary wavke solutions of BS(1,n) equations,compacton solutions of BS(m,m-1) equations and the compacton-like solution of the potential form (called PBS(3,2)) ωxt b(ux^m)xxy 4b(ωx^nωy)x=0.In addition,we show that the variable ∫^x uy dx admits dromion solutions rather than the field u itself in BS(1,n) equation.  相似文献   

13.
殷久利  田立新 《物理学报》2004,53(9):2821-2827
研究一类非线性方程,即广义Camassa-Holm方程C(n):ut+kux+β1u\{xxt\}+β2u\{n+1\}x+β3uxun\{xx\}+β4uun\{xxx\}=0.通过四种拟设得到丰富的精确解,特别是当k≠0时得到了com pacton解,当k=0时得到了移动compacton解.最后利用线 性化的方法得到了其他形式的广义Camassa-Holm方程的compacton解. 关键词: 广义Camassa-Holm方程 compacton解 移动compacton解  相似文献   

14.
In this paper, with the help of symbolic computation, a new Backlund transformation (BT) for a newgeneralized Zakharov-Kuznetsov equation with nonlinear term of any order, ut+aupux +bu2pux +γuxy +δuxxx +ρuxyy=0, is obtained by using the homogeneous balance method. Based on the BT, some exact solutions are presented.  相似文献   

15.
碱卤晶体热导率与压强的关系   总被引:1,自引:1,他引:0       下载免费PDF全文
 本文指出,关于碱卤晶体热导率λ与压强p之间关系的经验方程:λ=A+Bp或λ=A+Bp+Cp2,可以由Bridgman参量的定义g=-(d lnλ/dlnV)T和Tait方程ΔV/V0=ln(1+βp)/α导出。  相似文献   

16.
Searching for special solitary wave solutions with compact support is of important significance in soliton theory. In this paper, to understand the role of nonlinear dispersion in pattern formation, a family of the regularized longwave Boussincsq equations with fully nonlinear dispersion (simply called R(m, n) equations), utt + a( un )xx + b(um )xxtt = 0(a, b const.), is studied. New solitary wave solutions with compact support of R(m, n) equations are found. In addition we find another compacton solutions of the two special cases, R(2, 2) equation and R(3, 3) equation. It is found that the nonlinear dispersion term in a nonlinear evolution equation is not a necessary condition of that it possesses compacton solutions.  相似文献   

17.
In this paper, we qualitatively study radial solutions of the semilinear elliptic equation Δu+un = 0 with u(0) = 1 and u′(0) = 0 on the positive real line, called the Emden–Fowler or Lane–Emden equation. This equation is of great importance in Newtonian astrophysics and the constant n is called the polytropic index.

By introducing a set of new variables, the Emden–Fowler equation can be written as an autonomous system of two ordinary differential equations which can be analyzed using linear and nonlinear stability analysis. We perform the study of stability by using linear stability analysis, the Jacobi stability analysis (Kosambi–Cartan–Chern-theory) and the Lyapunov function method. Depending on the values of n these different methods yield different results. We identify a parameter range for n where all three methods imply stability.  相似文献   

18.
林岳明  何慧娟 《光学学报》1997,17(6):17-722
用RKR(Rydberg-Kleinn-Rees)方法计算了Cs2分子的X^1∑g和A^1∑u的势能曲线,求解了Cs2分子核运动的径向薛定谔方程,获得X态与A态间跃迁的Franck-Condon因子和1.06μm附近区域的吸收光谱,并与实验测得的吸收光谱作了比较,两者相当符合。  相似文献   

19.
Based on the computerized symbolic system Maple, a new generalized expansion method of Riccatiequation for constructing non-travelling wave and coefficient functions‘ soliton-like solutions is presented by a new generalansatz. Making use of the method, we consider the (2 1)-dimensional breaking soliton equation, ut buxxy 4buvx 4buxv = 0, uy = vx, and obtain rich new families of the exact solutions of the breaking soliton equation, including thenon-travelling wave and constant function soliton-like solutions, singular soliton-like solutions, and triangular functionsolutions.  相似文献   

20.
张文玲  马松华  陈晶晶 《物理学报》2014,63(8):80506-080506
借助Maple符号计算软件,利用Pdccati方程(ζ′=a_0+a_1ζ+a_2ζ~2)展开法和变量分离法,得到了(2+1)维Korteweg-de Vries方程(KdV)包含q=C_1x+C_2y+C_3t+R(x,y,t)的复合波解,根据得到的孤立波解,构造出KdV方程新颖的复合波裂变和复合波湮灭等局域激发结构。  相似文献   

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