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研究了一个强非线性波动方程.利用泛函分析变分迭代方法,首先构造了一个变分, 求出相应的Lagrange乘子;其次构造一个解的变分迭代, 选取初始孤子波;最后利用迭代方法依次求出各次孤子波的近似解.该方法是一个简单可行的近似求解非线性方程的方法 相似文献
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Jaulent-Miodek方程的行波解分支 总被引:1,自引:0,他引:1
利用平面动力系统分支理论研究了耦合的Jaulent-Miodek方程的孤立波及周期波的存在性,求出了分支参数集.在给定的参数条件下,得到了该方程光滑孤立波解及周期行波解的所有可能的显式表达式. 相似文献
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一类非线性非局部扰动LGH方程的孤子行波解 总被引:3,自引:3,他引:0
利用经过改进的泛函分析变分迭代方法讨论了一类非线性非局部Landau-Ginzburg-Higgs(LGH)微分方程.首先,做行波变换,引入泛函,并求出其变分,令其为0,得到了Lagrange(拉格朗日)算子应满足的条件,并求出它.然后,引入一个经过改进的变分迭代式,选取初始迭代函数为对应的无扰动LGH方程的孤子解.最后,利用迭代式依次得到非线性非局部LGH扰动方程求出各次孤子行波的渐近解和LGH扰动方程的精确解.通过一个例子说明了用经过改进的泛函分析变分迭代方法得到求解是有效的方法. 相似文献
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In this paper, many new explicit and exact travelling wave solutions for Burgers-Kolmogorov-Petrovskii-Piscounov(Burgers-KPP) equations are obtained by using hyperbola function method and Wu-elimination method, which include new singular solitary wave solutions and periodic solutions. Particular important cases of the equation, such as the generalized Burgers-Fisher equation, Burgers-Chaffee infante equation and KPP equation, the corresponding solutions can be obtained also. The method can also solve other nonlinear partial differential equations. 相似文献
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Potential Analysis - We prove absolute continuity of the law of the solution, evaluated at fixed points in time and space, to a parabolic dissipative stochastic PDE on L2(G), where G is an open... 相似文献
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《数学的实践与认识》2015,(16)
借助于计算机代数系统Mathematica,利用推广的简单方程方法构造了(2+1)维Broer-Kaup-Kupershmidt方程组的新的精确行波解,分别以含有双参数的用双曲函数,三角函数和有理函数表示,其中双曲函数表.示的行波解中参数取特殊值时可得到文献已有的孤波解.方法也适用于其它非线性发展方程(组). 相似文献
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In this paper by using upper-lower solution method, under appropriate assumptions on f and g the existence of travelling wave front solutions for the following reaction-diffusion system is proved: {u_t - u_{xx}, = f(u,v) v_t - v_{xx} = g(u, v) As an application, the necessary and sufficient condition of the existence of monotone solutions for the boundary value problem {u" + cu' + u(1 - u- rv) = 0 v" + cv' - buv = 0 u(-∞) = v(+∞) = 0 u(+∞) = v(-∞) = 1 where 0 < r < 1, 0 < b < \frac{1 - r}{r} are known constants and c is unknown constant to be obtained. 相似文献
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§1. IntroductionIn[1,2],AronsonandWeinbergerhavestudiedsystematiclythescalarnonlineardiffu-sionequationinonespacevariableut=uxx+φ(u),(1.1)whereu=u(x,t)andφ(u)isanonlinearfunction.Equation(1.1)arisesinseveralapplica-tions;See[1,2]and[3]forinformationa… 相似文献
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§ 1.Introduction Inthispaperwestudythestrongandweakpropertyoftravellingwavefrontsolutions (TWFS)forthefollowingdegenerateparabolicequation : ψ(u) t = 2 u x2 +f(u) . ( 1 .1 ) Welookforsolutionsof( 1 .1 )oftheformu(x,t) =q(x -ct) (cisthewavespeed) ,whereq( ξ) ,ξ=x -ct,asafunctionofas… 相似文献
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This work studies the finite-time blow-up of solutions to the equation utt−Δu=F(u) in Minkowski space. We develop a new technique which simplifies some of the existing arguments. The approach we use is a modification of the so-called method of conformal compactification. In this we are motivated by the work of Christodoulou, and Baez, Segal, and Zhou on nonlinear wave equations, as well as the recent developments in the rigorous theory of nonlinear quantum fields. 相似文献
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Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents北大核心CSCD
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该文考虑了一类带有变指数非局部项的反应扩散方程的爆破问题。首先,由不动点原理,证明了问题解的局部存在性和唯一性。其次,利用上下解方法,给出在齐次Dirichlet边界条件下,问题的解在有限时间发生爆破的充分条件,即变指数大于零且初始值足够大,并对爆破时间的上下界进行了估计。 相似文献