Anatomy of the Akhmediev breather: Cascading instability, first formation time, and Fermi-Pasta-Ulam recurrence
Anatomy of the Akhmediev breather: Cascading instability, first formation time, and Fermi-Pasta-Ulam recurrence
By invoking Bogoliubov's spectrum, we show that for the nonlinear Schr\"odinger equation, the modulation instability (MI) of its $n=1$ Fourier mode on a finite background automatically triggers a further cascading instability, forcing all the higher modes to grow exponentially in locked step with the $n=1$ mode. This fundamental insight, the …