FRIEDRICHS SYSTEMS FOR THE THREE-DIMENSIONAL WAVE EQUATION

V. M. Gordienko

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FRIEDRICHS SYSTEMS FOR THE THREE-DIMENSIONAL WAVE EQUATION

机译：三维波方程的弗里德里希系统

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The three-dimensional wave equation is reduced to a Friedrichs symmetric hyperbolic system. We describe all these reductions and find those of them that preserve the velocity of propagation of perturbations. We also exhibit transformations of a Friedrichs system under the Lorentz transformation of coordinates. The construction of the reduction of the wave equation and justification of the properties of this reduction are based on the use of quaternions.

机译：三维波动方程简化为Friedrichs对称双曲系统。我们描述了所有这些减少量，并找到其中的那些减少了扰动传播的速度。我们还展示了Lorentz坐标变换下的Friedrichs系统的变换。波动方程约简的构造和这种约简性质的合理性是基于四元数的使用。

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《Siberian Mathematical Journal》 |2010年第6期|共15页
作者
V. M. Gordienko;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
wave equation; Friedrichs hyperbolic system; quaternion;

机译：波动方程;Friedrichs双曲系统;四元数;

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1. FRIEDRICHS SYSTEMS FOR SYSTEMS OF WAVE EQUATIONS AND SHEAR WAVES IN A THREE-DIMENSIONAL ELASTIC MEDIUM [J] . Yu. A. Chirkunov Journal of Applied Mechanics and Technical Physics . 2010,第6期

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2. Friedrichs systems equivalent to the systems of wave equations [J] . Chirkunov Y.A. Journal of applied and industrial mathematics . 2012,第2期

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3. Calculation and optimization of three-dimensional waveguide systems by the integral equation method [J] . A. P. Gashturi, G. G. Denisov, S. V. Mishakin, Radiophysics and quantum electronics . 2008,第9期

机译：积分方程法计算和优化三维波导系统
4. Numerical solution of the one dimentional shallow water wave equations using finite difference method: Lax-Friedrichs scheme [C] . V. A. Riestiana, R. Setiyowati, V. Y. Kurniawan International Conference on Mathematics . 2021

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6. Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP BKP and CKP equations [O] . Wei Fu, Frank W. Nijhoff -1

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FRIEDRICHS SYSTEMS FOR THE THREE-DIMENSIONAL WAVE EQUATION

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