Inviscid traveling waves of monostable nonlinearity

Inviscid traveling waves are ghost-like phenomena that do not appear in reality because of their instability. However, they are the reason for the complexity of the traveling wave theory of reaction-diffusion equations and understanding them will help to resolve related puzzles. In this article, we obtain the existence, the uniqueness and the regularity of inviscid traveling waves under a general monostable nonlinearity that includes non-Lipschitz continuous reaction terms. Solution structures are obtained such as the thickness of the tail and the free boundaries.