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Abstract: Using symmetry analysis we systematically present a higher-dimensionalsimilarity transformation reducing the 3+1-dimensional inhomogeneousnonlinear Schrodinger NLS equation with variable coefficients and parabolicpotential to the 1+1-dimensional NLS equation with constant coefficients.This transformation allows us to relate certain class of localized exactsolutions of the 3+1-dimensional case to the variety of solutions ofintegrable NLS equation of 1+1-dimensional case. As an example, weillustrated our technique using two lowest order rational solutions of the NLSequation as seeding functions to obtain rogue wave-like solutions localized inthree dimensions that have complicated evolution in time including interactionsbetween two time-dependent rogue wave solutions. The obtained three-dimensionalrogue wave-like solutions may raise the possibility of relative experiments andpotential applications in nonlinear optics and BECs.



Autor: Zhenya Yan, V. V. Konotop, N. Akhmediev

Fuente: https://arxiv.org/



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