This paper considers the exact solution of Burgers’ hierarchy of nonlinear evolution equations. We construct the general nth conservation law of the hierarchy and prove that these expressions may be transformed into ordinary differential equations. In particular, a coordinate transformation leads to the systematic reduction of the conservation law properties of the Burgers’ hierarchy. Such an approach yields a nonlinear equation, where a second transformation is derived to linearize the expression. Consequently, this approach describes a procedure for finding the exact solutions of the hierarchy. A formula of the nth solution is provided, and to demonstrate its application, we discuss the solution to several members of the nonlinear hierarchy.

本文考虑了Burgers非线性演化方程层次的精确解。我们构造了层次的一般n守恒律，并证明了这些表达式可以转化为常微分方程。特别是，坐标转换导致系统地降低了伯格斯层次的守恒定律特性。这种方法产生一个非线性方程，在其中导出第二个变换以使表达式线性化。因此，此方法描述了用于查找层次结构的确切解决方案的过程。提供了第n个解决方案的公式，并且为了说明其应用，我们讨论了非线性层次结构中几个成员的解决方案。