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 by testing for the existence of 3- and 4-soliton solutions, and list the results that have been obtained this way for the KdV, mKdV/sG and nlS classes of equations.
CITATION STYLE
Integrability of Nonlinear Systems. (1997). Integrability of Nonlinear Systems. Springer Berlin Heidelberg. https://doi.org/10.1007/bfb0113690
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