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We construct new exact solutions of the focusing Nonlinear Schr"{o}dinger equation (NLSE). This is a soliton propagating on an unstable condensate. The Kuznetsov and Akhmediev solitons as well as the Peregrine instanton are particular cases of this new solution. We discuss applications of this new solution to the description of freak (rogue) waves in the ocean and in optical fibers.

生成讲解博客的中文版本

生成AI智能校验的中文版本