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On the stability of N-solitons in integrable systems

The dynamical stability of reflectionless N-solitons for a large class of integrable systems is considered. The underlying eigenvalue problem is the Zakharov–Shabat problem on for any r ≥ 1. Physical examples of interest include the vector nonlinear Schrödinger equation and the integrable (r + 1)-wave interaction problem. It is shown herein that under appropriate assumptions that these solitons are realized as a local minimum of an appropriate Lyapunov function, and are hence dynamically stable.