共查询到20条相似文献,搜索用时 46 毫秒
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本文研究了一类广义Zakharov方程的精确解行波解的问题.利用改进的G/G展开方法,借助于计算机代数系统Mathematica,获得了具有重要物理背景的广义Zakharov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,以及有理函数解. 相似文献
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首先给出了运输问题最优解的相关概念,将最优解扩展到广义范畴,提出狭义多重最优解和广义多重最优解的概念及其区别.然后给出了惟一最优解、多重最优解、广义有限多重最优解、广义无限多重最优解的判定定理及其证明过程.最后推导出了狭义有限多重最优解个数下限和广义有限多重最优解个数上限的计算公式,并举例验证了结论的正确性. 相似文献
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应用Riccati展开法,给出了非线性Konno-Oono方程的一系列新精确解.这些解的形式包括三角函数解、双曲函数解、有理函数解.最后,对特殊函数下的精确解进行数值模拟,给出这些精确解的直观表示. 相似文献
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在局部凸空间中引进了向量均衡问题的强超有效解、C-强超有效解、弱超有效解, C-弱超有效解、齐次超有效解、 C-齐次超有效解的概念,并在局部凸空间中用极理论为工具讨论了向量均衡问题的 C-弱超有效解, C-超有效解, C-齐次超有效解,以及C-强超有效解的对偶形式. 又在赋范线性空间中讨论了向量均衡问题的以上各种超有效解之间的等价性,并且在赋范线性空间具正规锥的条件下讨论了向量均衡问题的以上各种超有效解的对偶形式. 作为它的应用,给出了向量优化问题各种超有效解的对偶形式. 相似文献
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共振条件下一类方程无界解和周期解的共存性 总被引:1,自引:1,他引:0
讨论了在共振条件下一类具有等时位势的方程无界解和周期解的共存性.利用Poincare映射轨道的性质,给出了无界解的存在性条件.在此条件下,Poincare-Bohl定理,得到了方程的一个周期解,进而说明共振条件下这类方程无界解和周期解的是可以共存的.最后,给出了一个无界解和周期解共存的具有等时位势的方程实例. 相似文献
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应用辅助方程法求得Zakharov方程的精确解,这些解包括双曲函数解、三角函数解.当对双曲函数解中的参数取特殊值时,可得到孤立波解:当对三角函数解中的参数取特殊值时,可得到周期波函数解.实践表明:辅助方程法在非线性光学、量子光学、激光物理和等离子体物理等领域具有广泛的应用. 相似文献
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R. Bustamante R. W. Ogden 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):708-721
In the theory of nonlinear elasticity universal relations are relationships connecting the components of stress and deformation tensors that hold independently of the constitutive
equation for the considered class (or sub-class) of materials. They are classified as linear or nonlinear according as the
components of the stress appear linearly or nonlinearly in the relations. In this paper a general scheme is developed for
the derivation of nonlinear universal relations and is applied to the constitutive law of an isotropic Cauchy elastic solid.
In particular, we consider examples of quadratic and cubic universal relations. In respect of universal solutions our results confirm the general result of Pucci and Saccomandi [1] that nonlinear universal relations are necessarily generated
by the linear ones. On the other hand, for non-universal solutions we develop a general method for generating nonlinear universal
relations and illustrate the results in the case of cubic relations.
(Received: November 9, 2005) 相似文献
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G. Christakos 《Journal of Optimization Theory and Applications》1989,62(1):29-48
The concept of this work is that research on nonlinear modeling and estimation in a stochastic framework brings with it the study of the orthogonality structure of the probability densities involved. The connection is made by means of a probabilistic quantity, called the theta function, which under fairly broad integrability conditions defines the class of factorable random processes. These processes play a central role in the derivation of a recursive estimation scheme which is mathematically optimal and computationally attractive. The theory of factorable processes is simpler and its relevance to estimation practice is more direct than that of other sophisticated nonlinear approaches, such as martingales and Lie algebras.The author is indebted to Prof. D. R. Smith, University of California, San Diego, for helpful suggestions. 相似文献
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袁明生 《数学物理学报(B辑英文版)》2007,27(2):381-394
This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L∞norms, it analyzes the relative errors in approximate solutions. 相似文献
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J. R. Philip 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1994,45(3):387-398
Exact similarity solutions are developed for nonlinear diffusion with nonlinear reactive or irreversible absorptive loss from an instantaneous source. The diffusivity is proportional to a powerm of concentration, with 0 < m 1; and loss rate is also proportional to a power of concentration,n, with 0 n < 1. The solutions are for an arbitrary number of dimensionss > 0 withs=1, 2, 3 in physical applications. All solutions give the slug radius finite, increasing to a maximum, and then decreasing to zero in finite time. Withn < 1, the loss rate at small concentrations is large enough to ensure slug extinction in finite time. The corresponding exact solutions for gain, not loss, are given also. They become independent of initial slug quantity in the limit of infinite time. 相似文献
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In this paper, we deal with the global existence and nonexistence of solutions to a nonlinear diffusion system coupled via nonlinear boundary flux. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of nonnegative solutions. The critical curve of Fujita type is conjectured with the aid of some new results, which extend the recent results of Wang et al. [Nonlinear Anal. 71 (2009) 2134-2140] and Li et al. [J. Math. Anal. Appl. 340 (2008) 876-883] to more general equations. 相似文献
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Naoki Fujino 《Journal of Differential Equations》2006,228(1):171-190
We study scalar conservation laws with nonlinear diffusion and nonlinear dispersion terms (any ??1), the flux function f(u) being mth order growth at infinity. It is shown that if ε, δ=δ(ε) tend to 0, then the sequence {uε} of the smooth solutions converges to the unique entropy solution u∈L∞(0,T∗;Lq(R)) to the conservation law ut+fx(u)=0 in . The proof relies on the methods of compensated compactness, Young measures and entropy measure-valued solutions. Some new a priori estimates are carried out. In particular, our result includes the convergence result by Schonbek when b(λ)=λ, ?=1 and LeFloch and Natalini when ?=1. 相似文献
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Xia CuiGuang-wei Yuan Jing-yan Yue 《Journal of Computational and Applied Mathematics》2011,236(2):253-264
A nonlinear iteration method named the Picard-Newton iteration is studied for a two-dimensional nonlinear coupled parabolic-hyperbolic system. It serves as an efficient method to solve a nonlinear discrete scheme with second spatial and temporal accuracy. The nonlinear iteration scheme is constructed with a linearization-discretization approach through discretizing the linearized systems of the original nonlinear partial differential equations. It can be viewed as an improved Picard iteration, and can accelerate convergence over the standard Picard iteration. Moreover, the discretization with second-order accuracy in both spatial and temporal variants is introduced to get the Picard-Newton iteration scheme. By using the energy estimate and inductive hypothesis reasoning, the difficulties arising from the nonlinearity and the coupling of different equation types are overcome. It follows that the rigorous theoretical analysis on the approximation of the solution of the Picard-Newton iteration scheme to the solution of the original continuous problem is obtained, which is different from the traditional error estimate that usually estimates the error between the solution of the nonlinear discrete scheme and the solution of the original problem. Moreover, such approximation is independent of the iteration number. Numerical experiments verify the theoretical result, and show that the Picard-Newton iteration scheme with second-order spatial and temporal accuracy is more accurate and efficient than that of first-order temporal accuracy. 相似文献