New exact solutions to the nonautonomous Liouville equation

E. I. Semenov

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New exact solutions to the nonautonomous Liouville equation

机译：非自治Liouville方程的新精确解。

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We obtain new formulas for the exact analytic solutions to the nonautonomous elliptic Liouville equation in the two-dimensional coordinate space with the free function dependent specially on an arbitrary harmonic function. We present new exact solutions to the wave Liouville equation with two arbitrary functions, providing original formulas for the general solution for the classical (autonomous) and wave Liouville equations. Some equivalence transformations are presented for the elliptic Liouville equation depending on conjugate harmonic functions. In particular, we indicate a transformation that reduces the equation under study to an autonomous form.

机译：我们获得了具有自由函数特别依赖于任意谐波函数的二维坐标空间中非自治椭圆Liouville方程精确解析解的新公式。我们为带有两个任意函数的波动Liouville方程提供了新的精确解，为经典（自治）波动Liouville方程的一般解提供了原始公式。根据共轭谐波函数，给出了椭圆Liouville方程的一些等价变换。特别是，我们指出了一种转换方法，该方法可以将所研究的方程式简化为一个自治形式。

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《Siberian Mathematical Journal》 |2008年第1期|共9页
作者
E. I. Semenov;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
elliptic Liouville equation; wave Liouville equation; multidimensional exact solution; equivalence transformation; conjugate harmonic function;

机译：椭圆Liouville方程;波动Liouville方程;多维精确解;等价变换;共轭谐波函数;

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1. New exact solutions to the nonautonomous Liouville equation [J] . E. I. Semenov Siberian Mathematical Journal . 2008,第1期

机译：非自治Liouville方程的新精确解。
2. Exact solutions to nonlinear nonautonomous space-fractional diffusion equations with absorption - art. no. 051109 [J] . Lenzi EK., Mendes GA., Mendes RS., Physical review, E. Statistical physics, plasmas, fluids, and related interdisciplinary topics . 2003,第5aPta1期

机译：具有吸收的非线性非自治空间分数阶扩散方程的精确解-艺术。没有。 051109
3. EXACT SOLUTIONS OF LINEAR RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSES [J] . Agarwal Ravi P., Hristova Snezhana, ORegan Donal The Rocky Mountain journal of mathematics . 2020,第3期

机译：用冲动的线性Riemann-Liouville分数微分方程的精确解
4. Exact Solution of Two-Term Nonlinear Fractional Differential Equation with Sequential Riemann-Liouville Derivatives [C] . Marek Blasik, Malgorzata Klimek Conference on non-integer order calculus and its applications . 2013

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New exact solutions to the nonautonomous Liouville equation

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