329 citations · 5.2k across the 203 of their papers we have counts for
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Solitons and Vortices in Two-dimensional Discrete Nonlinear Schrodinger Systems with Spatially Modulated Nonlinearity
P. G. Kevrekidis, B. A. Malomed, A. Saxena +2
We consider a two-dimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defoc…
When Does Linear Stability Not Exclude Nonlinear Instability ?
P. G. Kevrekidis, D. E. Pelinovsky, A. Saxena
We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to…
PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators
J. Cuevas-Maraver, A. Khare, P. G. Kevrekidis +2
In the present work, we explore the case of a general PT-symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical hand…
Solitary Waves in a Discrete Nonlinear Dirac equation
J. Cuevas-Maraver, P. G. Kevrekidis, A. Saxena
In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross-Neveu model. The motivation for this discrete…
Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity
Sihong Shao, Niurka R. Quintero, Franz G. Mertens +3
We consider the nonlinear Dirac equation in 1+1 dimension with scalar-scalar self interaction and with mass . Using the exact analytic form…
Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations
Avinash Khare, Avadh Saxena
For a number of nonlocal nonlinear equations such as nonlocal, nonlinear Schrödinger equation (NLSE), nonlocal Ablowitz-Ladik (AL), nonlocal, saturable discrete NLSE (DNLSE), coupl…
Intrinsic Localized Modes of a Classical Discrete Anisotropic Heisenberg Ferromagnetic Spin Chain
M. Lakshmanan, B. Subash, Avadh Saxena
We report several exact intrinsic localized mode solutions of the classical spin evolution equation of a one-dimensional anisotropic Heisenberg ferromagnetic spin chain in terms of…