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We present a new type of soliton, found in models characterized by opposing dispersions a competing nonlinearities at fundamental and second harmonics. They are isolated solitary wav existing atâ€¦ (More)

It is commonly held that a necessary condition for the existence of solitons in nonlinear-wave systems is that the solitonâ€™s frequency (spatial or temporal) must not fall into the continuous spectrumâ€¦ (More)

- Rodislav Driben, Yi Hu, Zhigang Chen, Boris A. Malomed, R. Morandotti
- Optics letters
- 2013

By means of direct simulations and theoretical analysis, we study the nonlinear propagation of truncated Airy pulses in an optical fiber exhibiting both anomalous second-order and strong positiveâ€¦ (More)

- H. Sakaguchi, Ben Li, Boris A. Malomed
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2014

It is commonly known that two-dimensional mean-field models of optical and matter waves with cubic self-attraction cannot produce stable solitons in free space because of the occurrence of collapseâ€¦ (More)

We study the existence, stability, and mobility of fundamental discrete solitons in twoand three-dimensional nonlinear SchrÃ¶dinger lattices with a combination of cubic self-focusing and quinticâ€¦ (More)

- A. S. Desyatnikov, Dumitru Mihalache, Dumitru Mazilu, Boris A. Malomed, Cornelia Denz, Falk Lederer
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2005

We demonstrate that two-dimensional two-component bright solitons of an annular shape, carrying vorticities (m,+/-m) in the components, may be stable in media with the cubic-quintic nonlinearity,â€¦ (More)

We develop the technique of the variational approximation for solitons in two directions. First, one may have a physical model which does not admit the usual Lagrangian representation, as some termsâ€¦ (More)

- Andrey E Miroshnichenko, Sergej Flach, Boris A. Malomed
- Chaos
- 2003

We study the scattering of solitons in the nonlinear SchrÃ¶dinger equation on local inhomogeneities which may give rise to resonant transmission and reflection. In both cases, we derive resonanceâ€¦ (More)

A model of two coupled Ablowitz-Ladik (AL) lattices is introduced. While the system as a whole is not integrable, it admits reduction to the integrable AL model for symmetric states. Stability andâ€¦ (More)

Three-wave solitons and continuous waves in media with competing quadratic and cubic nonlinearities.

- Min Chen, D. J. Kaup, Boris A. Malomed
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2004

We formulate a general model of three-wave optical interactions (in the spatial domain), which combines quadratic (chi(2)) and cubic (chi(3)) nonlinearities, the latter including four-wave mixing.â€¦ (More)