Nonlinear equations linearized using the generalized Cole-Hopf substitutions and the exactly integrable models of the one-dimensional compressible fluid flows

Zhuravlev VM; Zinovev DA

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Nonlinear equations linearized using the generalized Cole-Hopf substitutions and the exactly integrable models of the one-dimensional compressible fluid flows

机译：使用广义Cole-Hopf替换和一维可压缩流体的精确可积分模型线性化的非线性方程

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摘要

A new method to derive the nonlinear equations linearized using the substitutions extending the Cole-Hopf substitution to the Burgers equation is considered. A method to analyze the general structure of the solutions and to calculate the exact solutions in the problems of one-dimensional compressible fluid flows is developed on the basis of this approach. The cases of the ideal and viscous fluids are considered. The problem of the dynamics of dust-like matter at a zero pressure and the gas-dust mixture is analyzed.

机译：考虑一种新的导出非线性方程的方法，该方法使用将Cole-Hopf替换扩展到Burgers方程的替换线性化。在这种方法的基础上，提出了一种分析溶液的一般结构并计算一维可压缩流体流动问题的精确解的方法。考虑理想流体和粘性流体的情况。分析了粉尘状物质在零压力和气体-粉尘混合物下的动力学问题。

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《JETP Letters》 |2008年第5期|共5页
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Zhuravlev VM; Zinovev DA;
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正文语种 eng
中图分类物理学;
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专利

1. Nonlinear equations linearized using the generalized Cole-Hopf substitutions and the exactly integrable models of the one-dimensional compressible fluid flows [J] . Zhuravlev VM, Zinovev DA JETP Letters . 2008,第5期

机译：使用广义Cole-Hopf替换和一维可压缩流体的精确可积分模型线性化的非线性方程
2. Nonlinear Waves in Self-Gravitating Compressible Fluid and Generalized Cole-Hopf Substitutions [J] . V. M. Zhuravlev, D. A. Zinov’ev Physics of wave phenomena . 2011,第4期

机译：自引力可压缩流体和广义Cole-Hopf置换中的非线性波
3. A Lumped-Parameter Modeling Methodology for One-Dimensional Hyperbolic Partial Differential Equations Describing Nonlinear Wave Propagation in Fluids [J] . Stockar Stephanie, Canova Marcello, Guezennec Yann, Journal of Dynamic Systems, Measurement, and Control . 2015,第1期

机译：一维双曲型偏微分方程描述流体中非线性传播的集总参数建模方法
4. Global solvability of the initial boundary value problem for a model system of one-dimensional equations of polytropic flows of viscous compressible fluid mixtures [C] . Dmitriy Prokudin All-Russian Conference with International Participation on Modern Problems of Continuum Mechanics and Explosion Physics . 2017

机译：粘性可压缩流体混合物多维方程模型系统的初步边值问题的全局可解性
5. Pfaffian and Wronskian solutions to generalized integrable nonlinear partial differential equations. [D] . Asaad, Magdy G. 2012

机译：广义可积非线性偏微分方程的Pfaffian和Wronskian解。
6. On Behrbohm and Pinls Linearization of the Equation of Two-Dimensional Steady Polytropic Flow of a Compressible Fluid [O] . C. Truesdell 1946

机译：关于可压缩流体二维稳态多相流方程的Behrbohm和Pinl线性化
7. Nonperiodic Flow in the Numerical Integration of a Nonlinear Differential Equation of Fluid Dynamics [O] . DeJesus, Edmund X., Kaufman, Charles 1985

机译：流体动力学非线性微分方程数值积分中的非周期性流动

Nonlinear equations linearized using the generalized Cole-Hopf substitutions and the exactly integrable models of the one-dimensional compressible fluid flows

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