Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

Abstract

We present determinant expressions for vector rogue wave solutions of the Manakov system, a two-component coupled nonlinear Schrödinger equation. As special case, we generate a family of exact and non-symmetric rogue wave solutions of the nonlinear Schrödinger equation up to third-order, localized in both space and time. The derived non-symmetric doubly-localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified nonlinear Schrödinger equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep-water.

arXiv comment15 pages, 7 figures, accepted by Proceedings of the Royal Society A

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