Hamiltonian form of the cubic nonlinear Schrodinger equations
= Hamiltonian form of the cubic nonlinear Schrodinger equations
{c}
The focusing and defocusing equations
$$
i\psi_t+\psi_{xx}\mathbin{\pm}2|\psi|^2\psi=0
$$
have Hamiltonians
$$
H_\pm=\int_{\mathbb R}\left(|\psi_x|^2\mp|\psi|^4\right)dx
$$
under the convention $i\psi_t=\delta H_\pm/\delta\overline\psi$.