摘要
We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations withmixed partial derivatives.As an application,we classify equations u_(xt)=A(u,u_x)u_(xxx)+B(u,u_x) that admits derivative-dependent functional separable solutions (DDFSSs) and illustrate how to construct those DDFSSs with some examples.
We present basic theory of variable separation for （1 ＋ 1）-dimensional nonlinear evolution equations with mixed partial derivatives. As an application, we classify equations uxt = A（u, ux）uxxx ＋ B（u, ux） that admits derivativedependent functional separable solutions （DDFSSs） and illustrate how to construct those DDFSSs with some examples.
基金
National Natural Science Foundation of China under Grant Nos.10447007 and 10671156
the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
关键词
空间非线性方程式
变数分离
对称方程式
派生物
（1 ＋ 1）-dimensional nonlinear evolution equations, variable separation, generalized conditional symmetry, derivative-dependent functional separable solution
