Abstract

We utilise the invariant method for scalar linear (1+1) parabolic partial differential equations so as to effect reductions via invertible transformations to Lie canonical forms of the first and third types. This is performed for the one-factor commodity models that have parameters which are constants or dependent on the price of stock or the time. The unknown parameters of the equations are determined. New closed-form solutions for the simple transformed equations are deduced by utilizing the equivalence maps and known solutions of the two Lie canonical forms.

中文翻译：

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通过单因素商品模型的不变方法的封闭形式解决方案

摘要

我们对标量线性 (1+1) 抛物线偏微分方程使用不变方法，以便通过可逆变换到第一类和第三类 Lie 规范形式来实现约简。这是针对具有常数或依赖于股票价格或时间的参数的单因素商品模型执行的。确定方程的未知参数。利用等价映射和两个李正则形式的已知解，推导出简单变换方程的新闭式解。