Theoretical and experimental evidence of non-symmetric doubly localized rogue waves.
We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS 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 NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water.
Department of Mathematics , Ningbo University , Ningbo, Zhejiang 315211, People's Republic of China ; DAMTP , University of Cambridge , Cambridge CB3 0WA, UK.
Jingsong
J
He
Department of Mathematics , Ningbo University , Ningbo, Zhejiang 315211, People's Republic of China.
Lijuan
L
Guo
Department of Mathematics , Ningbo University , Ningbo, Zhejiang 315211, People's Republic of China.
Yongshuai
Y
Zhang
Centre for Ocean Engineering Science and Technology , Swinburne University of Technology , Hawthorn, Victoria 3122, Australia.
Amin
A
Chabchoub
Darboux transformation; non-symmetric rogue waves; nonlinear Schrödinger equation