arXiv 1706.095042017-06-28math-phcond-mat.softcond-mat.stat-mechhep-thmath.MP

变形导数变分法的推广及应用

Extension and Applications of a Variational Approach with Deformed Derivatives

J. Weberszpil, J. A. Helayël-Neto

备注：: 19 pages

摘要：

我们最近提出了一个扩展的标准变分法，包括变形衍生物的存在下，在拉格朗日的一个质点系和拉格朗日密度的场论模型。经典的欧拉-拉格朗日方程和哈密顿形式主义已重新评估这种方法。每当应用到一些物理系统，由此产生的动力学方程出来是在文献中发现的正确的，特别是与质量相关的，并与经典和量子力学系统的非线性方程。在本文中，我们将变分方法与变形导数的区间形式相结合来研究高阶耗散系统，并将其应用于具体情况，例如加速点电荷-这是Abraham-Lorentz-Dirac力的问题-随机动力学，如Langevin，对流-对流-反应和Fokker-Planck方程，Korteweg-de Vries方程，Landau-Lifshits-Gilbert方程和Caldirola-Kanai哈密顿量。通过考虑这些不同的应用，我们表明，在本文中研究的配方可能是一个简单的和有前途的路径处理耗散，非线性和随机系统通过变分方法。

英文摘要：

We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical Euler-Lagrange equations and the Hamiltonian formalism have been re-assessed in this approach. Whenever applied to a number of physical systems, the resulting dynamical equations come out to be the correct ones found in the literature, specially with mass-dependent and with non-linear equations for classical and quantum-mechanical systems. In the present contribution, we extend the variational approach with the intervalar form of deformed derivatives to study higher-order dissipative systems, with application to concrete situations, such as an accelerated point charge - this is the problem of the Abraham-Lorentz-Dirac force - to stochastic dynamics like the Langevin, the advection-convection-reaction and Fokker-Planck equations, Korteweg-de Vries equation, Landau-Lifshits-Gilbert equation and the Caldirola-Kanai Hamiltonian. By considering these different applications, we show that the formulation investigated in this paper may be a simple and promising path for dealing with dissipative, non-linear and stochastic systems through the variational approach.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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