 Hamiltonian form of the cubic nonlinear Schrodinger equations

ID: hamiltonian-form-of-the-cubic-nonlinear-schrodinger-equations

Codex  0 Created 2026-09-24 Updated 2026-09-24

The focusing and defocusing equations

i ψ_{t} + ψ_{xx} \pm 2∣ ψ ∣^{2} ψ = 0

H_{\pm} = \int_{R} (∣ ψ_{x} ∣^{2} \mp ∣ ψ ∣^{4}) d x

under the convention

i ψ_{t} = δ H_{\pm} / δ \overline{ψ}

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