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- M Ablowitz, I Bakirtas, B Ilan
- 2007

A similar type of nonlocal nonlinear Schrödinger (NLS) system arises in both water waves and nonlinear optics. The nonlocality is due to a coupling between the first harmonic and a mean term. These systems are termed nonlinear Schrödinger with mean or NLSM systems. They were first derived in water waves by Benney-Roskes and later by Davey-Stewartson.… (More)

A nonlinear model of spin-wave excitation using a point contact in a thin ferromagnetic film is introduced. Large-amplitude magnetic solitary waves are computed, which help explain recent spin-torque experiments. Numerical simulations of the fully nonlinear model predict excitation frequencies in excess of 0.2 THz for contact diameters smaller than 6 nm.… (More)

We consider a class of nonlinear Schrödinger/Gross–Pitaevskii (NLS/GP) equations with periodic potentials having an even symmetry. We construct " solitons, " centered about any point of symmetry of the potential. For focusing (attractive) nonlinearities, these solutions bifurcate from the zero state at the lowest band-edge frequency into the semi-infinite… (More)

- M A Hoefer, B Ilan
- 2009

Dispersive shock waves ͑DSWs͒ are studied theoretically in the context of two-dimensional ͑2D͒ supersonic flow of a superfluid. Employing Whitham averaging theory for the repulsive Gross-Pitaevskii ͑GP͒ equation, suitable jump and entropy conditions are obtained for an oblique DSW, a fundamental building block for 2D flows with boundaries. In analogy to… (More)

- M A Hoefer, B Ilan
- 2016

We investigate propagating dark soliton solutions of the two-dimensional defocusing nonlinear Schrödinger or Gross-Pitaevskii (NLS-GP) equation that are transversely confined to propagate in an infinitely long channel. Families of single, vortex, and multilobed solitons are computed using a spectrally accurate numerical scheme. The multilobed solitons are… (More)

The nature of transverse instabilities of dark solitons for the (2+1)-dimensional defo-cusing nonlinear Schrödinger/Gross–Pitaevski ˘ i (NLS/GP) equation is considered. Special attention is given to the small (shallow) amplitude regime, which limits to the Kadomtsev–Petviashvili (KP) equation. We study analytically and numerically the eigenvalues of the… (More)

- M J Ablowitz, B Ilan, E Schonbrun, R Piestun
- 2007

We compute and study localized nonlinear modes (solitons) in the semi-infinite gap of the focusing two-dimensional nonlinear Schrödinger (NLS) equation with various irregular lattice-type potentials. The potentials are characterized by large variations from periodicity, such as vacancy defects, edge dislocations, and a quasicrystal structure. We use a… (More)

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