Waves play an important role in various applications and are an essential topic in modern applied mathematics.

This is an introductory course on the analysis of traveling waves and several other special solutions to nonlinear partial differential equations (PDEs).

Its core theme is the examination of their existence and stability, which can be carried out through a blend of techniques from dynamical systems theory, functional analysis, spectral theory and ordinary differential equations.

Prerequisites

Apart from a general background in mathematical analysis, the course has no prerequisites, all necessary tools from neighboring fields are introduced during the lecture.