Introduction to the Hirota bilinear method

We give an elementary introduction to Hirota’s direct method of constructing multisoliton solutions to integrable nonlinear evolution equations. We discuss in detail how this works for equations in the Korteweg-de Vries class. We also show how Hirota’s method can be used to search for new integrable evolution equations and list the results that have been obtained before for the mKdV/sG and nlS classes.

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