Abstract
The Hirota’s bilinear method [1] is now an important part of soliton theory (for reviews see e.g. [2,3,4]). The idea behind it is to use some transformation to put the nonlinear evolution equation (NEE) in a form which is quadratic in the dependent variable(s) and where derivatives appear only through the bilinear operator defined below. In this form the construction of soliton solutions is much easier.
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References
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In the Hirota form the soliton solutions are expressed in terms of finite sums of exponentials and the solution is therefore as regular as one can hope. This suggests the idea that the Hirota substitution for a NEE could be found by looking for a transformation that eliminates all singularities, see M. Kruskal and J. Hietarinta, work in progress.
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© 1990 Springer-Verlag Berlin, Heidelberg
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Hietarinta, J. (1990). Equations That Pass Hirota’s Three-Soliton Condition and Other Tests of Integrability. In: Carillo, S., Ragnisco, O. (eds) Nonlinear Evolution Equations and Dynamical Systems. Research Reports in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84039-5_8
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