214 research outputs found
Spectral Stability Analysis for Standing Waves of a Perturbed Klein-Gordon Equation
In the present work, we introduce a new PT -symmetric variant of the Klein-Gordon field theoretic problem. We identify the standing wave solutions of the proposed class of equations and analyze their stability. In particular, we obtain an explicit frequency condition, somewhat reminiscent of the classical VakhitovKolokolov criterion, which sharply separates the regimes of spectral stability and instability. Our numerical computations corroborate the relevant theoretical resul
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Kink-Antikink Interaction Forces and Bound States in a φ\u3csup\u3e4\u3c/sup\u3e Model with Quadratic and Quartic dispersion
In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of the nonlinear Schrödinger type bearing cubic nonlinearity. We present the first 6 families of multikink solutions and explore their bifurcations as the strength of the quadratic dispersion is varied. We reveal a rich bifurcation structure for the system, connecting two-kink states with states involving 4-, as well as 6-kinks. The stability of all of these states is explored. For each family, we discuss a “lower branch” adhering to the energy landscape of the 2-kink states. We also, however, study in detail the “upper branches” bearing higher numbers of kinks. In addition to computing the stationary states and analyzing their stability within the partial differential equation model, we develop an effective particle ordinary differential equation theory that is shown to be surprisingly efficient in capturing the kink equilibria and normal (as well as unstable) modes. Finally, the results of the bifurcation analysis are corroborated by means of direct numerical simulations involving the excitation of the states in a targeted way in order to explore their instability-induced dynamics
Kink-Antikink Interaction Forces and Bound States in a nonlinear Schr{\"o}dinger Model with Quadratic and Quartic dispersion
In the present work we explore the competition of quadratic and quartic
dispersion in producing kink-like solitary waves in a model of the nonlinear
Schr{\"o}dinger type bearing cubic nonlinearity. We present the first 6
families of multikink solutions and explore their bifurcations as the strength
of the quadratic dispersion is varied. We reveal a rich bifurcation structure
for the system, connecting two-kink states with states involving 4-, as well as
6-kinks. The stability of all of these states is explored. For each family, we
discuss a ``lower branch'' adhering to the energy landscape of the 2-kink
states. We also, however, study in detail the ``upper branches'' bearing higher
numbers of kinks. In addition to computing the stationary states and analyzing
their stability within the partial differential equation model, we develop an
effective particle ordinary differential equation theory that is shown to be
surprisingly efficient in capturing the kink equilibria and normal (as well as
unstable) modes. Finally, the results of the bifurcation analysis are
corroborated by means of direct numerical simulations involving the excitation
of the states in a targeted way in order to explore their instability-induced
dynamics
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