Travelling waves are observed in many natural processes, ranging from the spread of diseases to the combustion of fuels. A common feature of a multitude of these phenomena is that they can be similarly described in terms of a dispersive or diffusive mechanism, an advective or convective process, some kind of reaction, sorption, source or sink mechanism, or, an intricate balance between several of these factors. This book presents an overview of the occurence of travelling waves when these underlying phenomena can be mathematically modelled by a partial differential equation. The contents provide an up-to-date review of the state of the art in this field of research, touching on many different areas of application and including a large number of new results.

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