Integrable systems with quadratic nonlinearity in Fourier space
arXiv:nlin/0207022 · doi:10.1016/S0375-9601(03)00246-9
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.
6 pages