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Integrable systems with quadratic nonlinearity in Fourier space

V. G. Marikhin
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Abstract

The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The famous systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and A. Degasperis systems are represented in this list. Some new systems are obtained as well. The generalizations on two-dimensional and discrete systems are discussed.

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V. G. Marikhin. 2002-07-11. Integrable systems with quadratic nonlinearity in Fourier space. https://doi.org/10.1016/s0375-9601(03)00246-9

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