论文标题
关于非均匀分数汉堡方程与时间依赖的谐波振荡器之间的关系
On the relation between non-homogeneous fractional Burgers equations and time-dependent harmonic oscillator
论文作者
论文摘要
在本文中，我们讨论了与时间依赖性谐波电位的非均匀非均匀分数扩散方程与Schrodinger方程之间的关系。众所周知，Cole-Hopf转换允许将非均匀的非均质非线性扩散方程（NHNDES）线性化成具有时间依赖性电势的Schrodinger-type方程。我们首先讨论有关时间依赖性的谐波振荡器的结果的实用性，以构建这种非均匀的非均质偏微分方程的明确解。特别是，我们回想起，从NHNDE的试验多项式溶液开始，可以通过使用Schrodinger方程的线性不变性来构建其他溶液。最后，我们应用这些结果来找到新型非均匀分数汉堡型方程的明确解决方案。
In this paper we discuss the relation between non-homogeneous nonlinear fractional diffusive equations and the Schrodinger equation with time-dependent harmonic potential. It is well known that the Cole-Hopf transformation allows to linearize non-homogeneous nonlinear diffusive equations (NHNDEs) into a Schrodinger-type equation with time-dependent potential. We first discuss the utility of the results about time-dependent harmonic oscillator to build explicit solution of such non-homogeneous nonlinear partial differential equations. In particular, we recall that starting from a trial polynomial solution of the NHNDE, it is possible to construct other solutions by using linear invariants of the Schrodinger equation with time-dependent potential. Finally we apply these results to find explicit solutions to a novel non-homogeneous fractional Burgers-type equation.
