标题： 非线性一阶偏微分方程，其导数在多项式齐次中可化为自治形式 显示英文标题

标题： Nonlinear first order PDEs reducible to autonomous form polynomially homogeneous in the derivatives

摘要： 证明了一个定理，该定理提供了必要且充分的条件，使得可以将一个关于导数为多项式的首阶非线性偏微分方程组映射到一个等价的自治首阶多项式齐次的方程组。 该结果与源系统的对称性性质密切相关，证明过程中使用了与所接受的李点对称性相关的规范变量，具有构造性。 考虑了首阶Monge-Ampère系统，无论是具有常系数还是依赖于场变量的系数，该定理都可以成功应用。 显示英文摘要

摘要： It is proved a theorem providing necessary and sufficient conditions enabling one to map a nonlinear system of first order partial differential equations, polynomial in the derivatives, to an equivalent autonomous first order system polynomially homogeneous in the derivatives. The result is intimately related to the symmetry properties of the source system, and the proof, involving the use of the canonical variables associated to the admitted Lie point symmetries, is constructive. First order Monge-Amp\`ere systems, either with constant coefficients or with coefficients depending on the field variables, where the theorem can be successfully applied, are considered.