EuDML | Browse

This paper investigates adaptive switched modified function projective synchronization between two complex nonlinear hyperchaotic systems with unknown parameters. Based on adaptive control and parameter identification, corresponding adaptive controllers with appropriate parameter update laws are constructed to achieve switched modified function projective synchronization between two different complex nonlinear hyperchaotic systems and to estimate the unknown system parameters. A numerical simulation...

Symmetries of the nonlinear Schrödinger equation

Benoît Grébert, Thomas Kappeler (2002)

Bulletin de la Société Mathématique de France

Symmetries of the defocusing nonlinear Schrödinger equation are expressed in action-angle coordinates and characterized in terms of the periodic and Dirichlet spectrum of the associated Zakharov-Shabat system. Application: proof of the conjecture that the periodic spectrum $\dots < λ_{k}^{-} \leq λ_{k}^{+} < λ_{k + 1}^{-} \leq \dots$ of a Zakharov-Shabat operator is symmetric,i.e. $λ_{k}^{\pm} = - λ_{- k}^{\mp}$ for all $k$ , if and only if the sequence ${(γ_{k})}_{k \in ℤ}$ of gap lengths, $γ_{k} : = λ_{k}^{+} - λ_{k}^{-}$ , is symmetric with respect to $k = 0$ .

Displaying 1 – 8 of 8

Currently displaying 1 – 8 of 8