Travelling wave solutions to partial differential equations

In the world of mathematics, partial differential equations (abbreviated as PDEs) are used for modelling natural phenomena, from very basic transport and diffusion processes (e.g. kinetic transport of gas molecules inside a closed system), to more complicated physical processes (such as fluid dynamics around complicated geometries). These equations are often unsolvable analytically, and so we often employ powerful computers and specialized software in order to find approximate solutions. However, there are special cases in which analytic solutions to…