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

TL;DR

This paper derives and experimentally verifies non-symmetric doubly localized rogue wave solutions in the nonlinear Schrödinger equation, combining theoretical, numerical, and physical water wave experiments to demonstrate their characteristics.

Contribution

It provides the first explicit determinant expressions for non-symmetric rogue waves and confirms their existence through laboratory water wave experiments.

Findings

Experimental rogue wave patterns match theoretical predictions.

Non-symmetric rogue waves are localized in both space and time.

The solutions are validated by numerical simulations with the modified nonlinear Schrödinger equation.

Abstract

We present determinant expressions for vector rogue wave solutions of the Manakov system, a two-component coupled nonlinear Schr\"odinger equation. As special case, we generate a family of exact and non-symmetric rogue wave solutions of the nonlinear Schr\"odinger 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 Schr\"odinger equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep-water.