约化算子的分类与变系数Newell-Whitehead-Segel方程的精确解
Classification of reduction operators and exact solutions of variable coefficient Newell-Whitehead-Segel equations
摘要：
利用Lie和“非经典”对称性的观点研究了一类Newell-Whitehead-Segel方程（又称广义Fisher方程和Newell-Whitehead方程）.对李约化算子和正则非经典约化算子进行了分类。类的容许变换集（等价广群）被详尽地描述。导出了变系数Newell-Whitehead-Segel方程约化为常系数Newell-Whitehead-Segel方程的判据。广泛的家庭的精确解，这样的变系数方程的构造。
英文摘要：
A class of the Newell-Whitehead-Segel equations (also known as generalized Fisher equations and Newell-Whitehead equations) is studied with Lie and "nonclassical" symmetry points of view. The classifications of Lie reduction operators and of regular nonclassical reduction operators are performed. The set of admissible transformations (the equivalence groupoid) of the class is described exhaustively. The criterion of reducibility of variable coefficient Newell-Whitehead-Segel equations to their constant coefficient counterparts is derived. Wide families of exact solutions for such variable coefficient equations are constructed.
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