Abstract
A new hamiltonian amplitude equation, iψ x +ψ tt +2σ|ψ| 2 ψ-∈ψ xt =0 σ=±1, ∈<<1, is introduced. The equation governs certain instabilities of modulated wave-trains, and the addition of the term -∈ψ xt overcomes the ill-posedness of the unstable nonlinear Schrodinger equation. This new equation is apparently not integrable, but it is a Hamiltonian analogue of the Kuramoto-Sivashinsky equation, which arises in dissipative systems
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