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Artículo
Nonlinear Dirac equation solitary waves in external fields
(2012)
We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2κ+1(Ψ¯¯¯Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external ...
Artículo
Using the finite domain remnant of the continuous spectrum to examine integrability: Effect of boundary conditions
(2003)
The aim of this work is to propose a method for testing the integrability of a model partial differential (PDE) and/or differential difference equation (DDE), by examining it in a finite but large domain. For monoparametric ...
Artículo
Lagrangian Formalism in Perturbed Nonlinear Klein-Gordon Equations
(Elsevier, 2004)
We develop an alternative approach to study the effect of the generic perturbation (in addition to explicitly considering the loss term) in the nonlinear Klein–Gordon equations. By a change of the variables that cancel ...
Artículo
Nonequivalence of phonon modes in the sine-Gordon equation
(2001)
We study the resonances in the sine-Gordon equation driven by an ac force using a linear perturbation theory. We show that resonances take place when the driving frequency d is equal to half of the phonon modes’ frequencies ...
Artículo
Soliton ratchets in homogeneous nonlinear Klein-Gordon systems
(2006)
We study in detail the ratchetlike dynamics of topological solitons in homogeneous nonlinear Klein-Gordon systems driven by a biharmonic force. By using a collective coordinate approach with two degrees of freedom, namely ...
Artículo
Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity
(American Physical Society, 2014)
We consider the nonlinear Dirac equation in 1 + 1 dimension with scalar-scalar 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 ...
Artículo
Nonlinear Schrödinger equation with spatiotemporal perturbations
(2010)
We investigate the dynamics of solitons of the cubic nonlinear Schrödinger equation (NLSE) with the following perturbations: nonparametric spatiotemporal driving of the form f(x,t)=a exp[iK(t)x], damping, and a linear term ...
Artículo
Generalized traveling-wave method, variational approach, and modified conserved quantities for the perturbed nonlinear Schrödinger equation.
(2010)
The generalized traveling wave method (GTWM) is developed for the nonlinear Schrödinger equation (NLSE) with general perturbations in order to obtain the equations of motion for an arbitrary number of collective coordinates. ...
Artículo
Analytical approach to soliton ratchets in asymmetric potentials
(2005)
We use soliton perturbation theory and collective coordinate ansatz to investigate the mechanism of soliton ratchets in a driven and damped asymmetric double sine-Gordon equation. We show that, at the second order of the ...
Artículo
Forced nonlinear Schrödinger equation with arbitrary nonlinearity
(2012)
We consider the nonlinear Schrödinger equation (NLSE) in 1+1 dimension with scalar-scalar self-interaction 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 ...