Introduction to the Hirota Bilinear Method

Abstract

We give an elementary introduction to Hirota’s direct method of constructing multi-soliton solutions to integrable nonlinear evolution equations. We discuss in detail how this works for equations in the Korteweg–de Vries class, with some comments on the more complicated cases. We also show how Hirota’s method can be used to search for new integrable evolution equations and list some equations found this way.