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ABSTRACT: We study numerically rogue waves in the two-component Bose-Einstein condensates which are described by the coupled set of
two Gross-Pitaevskii equations with variable scattering lengths. We show that rogue wave solutions exist only for certain
combinations of the nonlinear coefficients describing two-body interactions. We present the solutions for the combinations
of these coefficients that admit the existence of rogue waves.
The European Physical Journal Special Topics 04/2012; 185(1):169-180. · 1.56 Impact Factor
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ABSTRACT: Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schrodinger (NLS) equation with variable coefficients and parabolic potential to the (1+1)-dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1)-dimensional case to the variety of solutions of integrable NLS equation of (1+1)-dimensional case. As an example, we illustrated our technique using two lowest order rational solutions of the NLS equation as seeding functions to obtain rogue wave-like solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wave-like solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and BECs. Comment: 7 pages, 6 figures
10/2010;
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[show abstract]
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ABSTRACT: Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1) -dimensional inhomogeneous nonlinear Schrödinger (NLS) equation with variable coefficients and parabolic potential to the (1+1) -dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1) -dimensional case to the variety of solutions of integrable NLS equation of the (1+1) -dimensional case. As an example, we illustrated our technique using two lowest-order rational solutions of the NLS equation as seeding functions to obtain rogue wavelike solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wavelike solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and Bose-Einstein condensates.
Physical Review E 09/2010; 82(3 Pt 2):036610. · 2.26 Impact Factor
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[show abstract]
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ABSTRACT: We study numerically rogue waves in the two-component Bose-Einstein condensates which are described by the coupled set of two Gross-Pitaevskii equa-tions with variable scattering lengths. We show that rogue wave solutions exist only for certain combinations of the nonlinear coefficients describing two-body interactions. We present the solutions for the combinations of these coefficients that admit the existence of rogue waves.
Eur. Phys. J. Special Topics EDP Sciences. 01/2010; 185:169-180.
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ABSTRACT: We predict the existence of rogue waves in Bose-Einstein condensates either loaded into a parabolic trap or embedded in an optical lattice. In the latter case, rogue waves can be observed in condensates with positive scattering length. They are immensely enhanced by the lattice. Local atomic density may increase up to tens times. We provide the initial conditions necessary for the experimental observation of the phenomenon. Numerical simulations illustrate the process of creation of rogue waves.
Phys. Rev. A. 09/2009; 80(3).
