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Vector rogue waves in the Manakov system: diversity and compossibility

2015; Institute of Physics; Volume: 48; Issue: 21 Linguagem: Inglês

10.1088/1751-8113/48/21/215202

1751-8121

Shihua Chen, Dumitru Mihalache,

Ocean Waves and Remote Sensing

We employ a nonrecursive Darboux transformation formalism for obtaining a hierarchy of rogue wave solutions to the focusing vector nonlinear Schrodinger equations (Manakov system). The exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple, quadruple, and sextuple vector rogue waves, either bright–dark or bright–bright in their respective components, are put forward. Despite the diversity, there exists a universal compossibility that different rogue wave states could coexist for the same background parameters. It is also shown that the higher-order rogue wave hierarchy can indeed be thought of as a nonlinear superposition of a fixed well prescribed number of fundamental rogue waves. These results may help understand the protean rogue wave manifestations in areas ranging from hydrodynamics to nonlinear optics.