Fibration of the Phase Space for the Periodic Non-Linear Schrödinger Equation and for the Periodic Toda Lattice Equations

We consider the defocusing cubic non-linear Schrödinger equation (NLS) i ∂ φ ∂ t ( x , t ) = − ∂ 2 φ ∂ x 2 ( x , t ) + 2 | φ ( x , t ) | 2 φ ( x , t ) , ( x , t ) ∈ ℝ 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072096/6e6221c8-364d-4a5e-bfe5-98bb034e69b7/content/eq167.tif"/>