Integrable systems with quadratic nonlinearity in Fourier space

Details Integrable systems with quadratic nonlinearity in Fourier space Integrable systems with quadratic nonlinearity in Fourier space

2002-07-11

arxiv.org/abs/nlin/0207022v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

6 pages

Scientific paper

10.1016/S0375-9601(03)00246-9

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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