Abstract
The bilinear method introduced by Hirota to obtain exact solutions for nonlinear evolution equations is discussed. Firstly, several examples including the Korteweg-deVries, nonlinear Schrödinger and Toda equations are given to show how solutions are derived. Then after considering multi-dimensional systems such as the Kadomtsev-Petviashvili, two dimensional Toda and Hirota-Miwa equations, the algebraic structure of such nonlinear evolution systems is explained. Finally, extensions of the method including q-analogue, ultra-discrete systems and trilinear forms are also presented.
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Satsuma, J. Hirota bilinear method for nonlinear evolution equations. In: Direct and Inverse Methods in Nonlinear Evolution Equations. Lecture Notes in Physics, vol 632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39808-0_4
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DOI: https://doi.org/10.1007/978-3-540-39808-0_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20087-1
Online ISBN: 978-3-540-39808-0
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