 Bright standing soliton of the focusing nonlinear Schrodinger equation

ID: bright-standing-soliton-of-the-focusing-nonlinear-schrodinger-equation

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

For every

κ > 0

and

x_{0} \in R

ψ (x, t) = κ e^{i κ^{2} t} sech (κ (x - x_{0}))

solves

i ψ_{t} + ψ_{xx} + 2∣ ψ ∣^{2} ψ = 0

and decays rapidly as

∣ x ∣ \to \infty

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