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- W2074330030 abstract "We construct a multi-parametric family of the solutions of the focusing nonlinear Schr?dinger equation (NLS) from the known results describing the multi-phase almost-periodic elementary solutions given in terms of Riemann theta functions. We give a new representation of their solutions in terms of Wronskians determinants of order 2N composed of elementary trigonometric functions. When we perform a special passage to the limit when all the periods tend to infinity, we obtain a family of quasi-rational solutions. This leads to efficient representations for the Peregrine breathers of orders N = 1,?2,?3 first constructed by Akhmediev and his co-workers and also allows us to obtain a simpler derivation of the generic formulas corresponding the three or six rogue-wave formation in the frame of the NLS model first explained by V B Matveev in 2010. Our formulation allows us to isolate easily the second- or third-order Peregrine breathers from ?generic? solutions and also to compute the Peregrine breathers of orders 2 and 3 easily with respect to other approaches. In the cases N = 2,?3, we obtain the comfortable formulas to study the deformation of a higher Peregrine breather of order 2 to the three rogue-wave or order 3 to the six rogue-wave solutions via the variation of the free parameters of our construction." @default.
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- W2074330030 date "2011-10-10" @default.
- W2074330030 modified "2023-09-26" @default.
- W2074330030 title "Families of quasi-rational solutions of the NLS equation and multi-rogue waves" @default.
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- W2074330030 doi "https://doi.org/10.1088/1751-8113/44/43/435204" @default.
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