Breathers and the weakly nonlinear NLS framework

BK_RW3At the end of Guido Schneider‘s talk, Victor Shrira spoke about recent work of his on validity of NLS from a different perspective.  He mentioned the recent paper On the highest non-breaking wave in a group: fully nonlinear water wave breathers versus weakly nonlinear theory.  This paper was interested in the highest possible wave in a wave group.  The question was addressed by comparing breather solutions of NLS with their counterparts in the full Euler equations. Breathers, the key basic elements of wave field evolution withing the NLS framework, are computed and extended to the full Euler equations. Direct numerical simulations of the full Euler equations were computed using both time-dependent conformal mapping and the HOSM approach. To create fully nonlinear counterparts to NLS breathers, the initial conditions for fully nonlinear simulations were taken in the form of a train of Stokes waves modulated in accordance with the exact breather solution of the NLS equation.  The fact that the breather-like structures survive in the fully nonlinear simulations and behave qualitatively like the NLS framework reveals that the underlying physics of the self-focusing effect remains qualitatively the same.

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