共查询到20条相似文献,搜索用时 0 毫秒
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D. G. Crowdy 《Journal of Nonlinear Science》1999,9(6):615-640
Summary. Exact solutions for steady capillary waves on an annulus of swirling irrotational fluid are presented. The solutions have
an intimate mathematical connection with the finite amplitude waves on fluid sheets identified by Kinnersley [8]. This mathematical
connection is made explicit by first retrieving the solutions of Kinnersley using an extension of a new approach to free surface
potential flows with capillarity recently devised by the present author (Crowdy [3]). A much-simplified representation of
Kinnersley's original solutions results from the reformulation. The method is then generalized to identify the exact solutions
for steady capillary waves on an annulus.
Received February 9, 1998; revised November 5, 1998 相似文献
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A quasi-linear nonhomogeneous first order hyperbolic system describing nerve pulse transmission is considered. By requiring the compatibility of the governing equations with quasi-linear differential constraints, exact solutions to the model in question are determined. Furthermore classes of material response functions amenable to the mathematical approach are characterized. Initial and/or boundary value problems of interest in nerve pulse propagation are solved. It is proved that the governing model admits solutions which describe a space clamp situation and the propagation of a localized action potential pulse along the nerve. 相似文献
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Exact traveling-wave solutions of time-dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs. 相似文献
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Doklady Mathematics - A new method for constructing exact solutions of nonlinear equations of mathematical physics is proposed. The method is based on nonlinear integral transformations in... 相似文献
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李林 《数学的实践与认识》2009,39(1)
研究一个描述血吸虫病的周期微分方程模型dx/dt=-rx+A/S(t)y,dy/dt=-δ(t)y+B(S(t)-y) x2/1+ x.数值计算发现该系统同时具有渐近稳定的零解和一个正周期解.通过证明该系统解的有界性,并在一个函数空间上构造单调有界序列,进而证明了在一定条件下正周期解的存在性. 相似文献
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A. R. Kessel R. R. Nigmatullin A. A. Khamzin N. A. Yakovleva 《Theoretical and Mathematical Physics》2005,145(3):1727-1735
For the model of equal spin-spin interactions, we obtain exact Heisenberg expressions for the spin operator components and
use them to find the relations that hold for spin operators appearing in the thermodynamic mean. We use the obtained exact
relations for the means to describe the thermodynamics of the model under consideration.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 411–419, December, 2005. 相似文献
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The classical Lie approach and the method of additional generating conditions are applied to constructing multiparameter families of exact solutions of the generalized Fisher equation, which is a simplification of the known coupled reaction–diffusion system describing spatial segregation of interacting species. The exact solutions are applied to solving nonlinear boundary-value problems with zero Neumann conditions. A comparison of the analytic results and the corresponding numerical calculations shows the importance of the exact solutions obtained for the solution of the generalized Fisher equation. 相似文献
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应用改进的简单方程法求得Cahn-Allen方程和Jimbo-Miwa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,可以得到了孤立波解.当对三角函数解中的参数取特殊值时,可以得到对应的周期波函数解.实践证明,简单方程法对于研究非线性数学物理方程具有非常广泛的应用意义. 相似文献
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Ronald E. Mickens 《Journal of Difference Equations and Applications》2013,19(11):995-1006
This article gives exact solutions to a finite-difference model of a nonlinear reaction-advection equation. We show that this partial difference equation and the corresponding stationary and spatially independent difference equations derived from this model give the best representation of the original partial differential equation. The relevance of this work to the elimination of chaotic behavior in numerical solutions of differential equations is discussed. 相似文献
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Catherine Choquet 《Acta Appl Math》2008,103(3):277-299
We consider a problem of nuclear waste contamination in the basement. We derive a detailed model describing the simultaneous
transport of brine, radionuclides and heat in a compressible flow through a porous medium. It leads to a nonlinear system
of fully coupled partial differential equations. Using a fixed point approach, we prove existence of physically relevant weak
solutions.
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The Existence of Global Solutions to a Fluid Dynamic Model for Materials for Korteweg Type 下载免费PDF全文
We discuss the existence of global solutions to a fluid dynamic model for materials of Korteweg type, and discuss the three dimensional nonisothermal motion. The higher order derivatives of density in the constitutive relation makes it necessary to introduce an interstitial working term in the energy equation. This makes the energy estimate more involved. Nevertheless, it is possible to show the existence of global solutions by the euergy method. 相似文献
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研究食道中蠕动传输的流体力学.对任意的波形和任意的管道长度,建立起流变学流体蠕动传输的数学模型.用粘性流体的Ostwald-de Waele幂定律,描述非Newton流体的流动特性.解析公式化模型,详细且精确地给出食物块在食道中蠕动传输相关的一些重要性质.分析中应用了润滑理论,本研究特别适合于Reynolds数不大的情况.将食道看作环形的管道,通过食道壁周期性的收缩来传输食物块.就单个波和周期性收缩一组波的传播,研究与传输过程有关变量的变化,如压力、流速、食物颗粒轨迹以及流量等.局部压力的变化,对流变指数n有着高度的敏感性.研究结果清晰地表明,食物块在食道中蠕动传输时,Newton流体或流变学流体构成的连续流体,以组合波传播比大间隔单波传播,传输效率要高得多. 相似文献
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RLW—Burgers方程的精确解 总被引:6,自引:0,他引:6
借助未知函数的变换,RLW-Burgers方程和KdV-Burgers方程化为易于求解的齐次形式的方程,从而得到RLW-Burgers方程和KdV-Burgers方程的精确解。 相似文献