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Browsing by Author "Khare, Avinash"
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Erratum: Nonlinear Dirac equation solitary waves in external fields [Phys. Rev. E 86, 046602 (2012)] [Article]
Mertens, Franz G.; Quintero, Niurka R.; Cooper, Fred; Khare, Avinash; Saxena, Avadh (American Physical Society, 2016) 
Forced nonlinear Schrödinger equation with arbitrary nonlinearity [Article]
Cooper, Fred; Khare, Avinash; Quintero, Niurka R.; Mertens, Franz G.; Saxena, Avadh (2012)We consider the nonlinear Schrödinger equation (NLSE) in 1+1 dimension with scalarscalar selfinteraction g2κ+1(ψ☆ψ)κ+1 in the presence of the external forcing terms of the form re−i(kx+θ)−δψ. We find new exact solutions ...

Interplay between paritytime symmetry, supersymmetry, and nonlinearity: An analytically tractable case example [Article]
Kevrekidis, Panayotis G.; CuevasMaraver, Jesús; Saxena, Avadh; Cooper, Fred; Khare, Avinash (American Physical Society, 2015)In the present work, we combine the notion of paritytime (PT ) symmetry with that of supersymmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the socalled P¨oschlTeller ...

Nonlinear Dirac equation solitary waves in external fields [Article]
Mertens, Franz G.; Quintero, Niurka R.; Cooper, Fred; Khare, Avinash; Saxena, Avadh (2012)We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalarscalar selfinteraction g2κ+1(Ψ¯¯¯Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external ...

Parametrically driven nonlinear Dirac equation with arbitrary nonlinearity [Article]
Cooper, Fred; Khare, Avinash; Quintero, Niurka R.; SánchezRey, Bernardo; Mertens, Franz G.; Saxena, Avadh (IOP Publishing, 202001)The damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter κ is analyzed, when the external force is periodic in space and given by f(x) = r cos(Kx), both numerically and in a ...

PT Symmetric dimer in a generalized model of coupled nonlinear oscillators [Article]
CuevasMaraver, Jesús; Khare, Avinash; Kevrekidis, Panayotis G.; Xu, Haitao; Saxena, Avadh (Springer, 2015)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 handle on the system, we first explore ...

PTsymmetric dimer of coupled nonlinear oscillators [Article]
CuevasMaraver, Jesús; Kevrekidis, Panayotis G.; Saxena, Avadh; Khare, Avinash (2013)We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from the linear limit of the ...

Response of exact solutions of the nonlinear Schrödinger equation to small perturbations in a class of complex external potentials having supersymmetry and paritytime symmetry [Article]
Cooper, Fred; Dawson, John F.; Mertens, Franz G.; Arévalo, Edward; Quintero, Niurka R.; Mihaila, Bogdan; Khare, Avinash; Saxena, Avadh (IOP, 2017)We discuss the effect of small perturbation on nodeless solutions of the nonlinear Schrödinger equation in 1 + 1 dimensions in an external complex potential derivable from a paritytime symmetric superpotential that ...

Solitary waves in the nonlinear Dirac equation in the presence of external driving forces [Article]
Mertens, Franz G.; Cooper, Fred; Quintero, Niurka R.; Sihong, Shao; Khare, Avinash; Saxena, Avadh (IOP, 2016)We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalarscalar selfinteraction in the presence of external forces as well as damping of the form f (x, t)  ιμγͦψ, where both f and ψ are twocomponent ...

Solitary waves of a PT symmetric Nonlinear Dirac equation [Article]
CuevasMaraver, Jesús; Kevrekidis, Panayotis G.; Saxena, Avadh; Cooper, Fred; Khare, Avinash; Comech, Andrew; Bender, Carl M. (IEEE, 2016)In the present work, we consider a prototypical example of a PT symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the PT phase transition in an analytical form. ...

Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity [Article]
Sihong, Shao; Quintero, Niurka R.; Mertens, Franz G.; Khare, Avinash; Saxena, Avadh (American Physical Society, 2014)We consider the nonlinear Dirac equation in 1 + 1 dimension with scalarscalar self interaction g2κ+1(Ψ¯¯¯Ψ)κ+1 and with mass m. Using the exact analytic form for rest frame solitary waves of the form Ψ(x,t)=ψ(x)e−iωt for ...