A general reaction–diffusion equation with nonlinear advection term having neither monotonicity nor variational structure is considered. This work is concerned with traveling waves for this type of equations. By constructing an invariant region with a lower curve smoothly connecting two fixed points where a heteroclinic orbit exists, we establish several theorems on the existence of wave fronts. The challenging problem on linear or nonlinear determinacy of the minimal speed is investigated. A necessary and sufficient condition for the nonlinear selection mechanism is obtained by a geometrical argument coupled with a perturbation method in a weighted functional space. On this basis, explicit sufficient conditions for the linear and nonlinear selection are derived. As applications, the claims or conjectures proposed in some important literature are rigorously proved.

考虑了具有既不具有单调性也不具有变分结构的非线性平流项的一般反应-扩散方程。这项工作与此类方程的行波有关。通过构造一个具有下曲线的不变区，平滑连接存在异宿轨道的两个固定点，我们建立了几个关于波前存在的定理。研究了关于最小速度的线性或非线性确定性的挑战性问题。非线性选择机制的充要条件是通过几何参数与加权函数空间中的微扰方法相结合得到的。在此基础上，推导出线性和非线性选择的显式充分条件。作为应用程序，