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We consider the stability problem for standing waves of nonlinear Dirac models. Under a suitable definition of linear stability, and under some restriction on the spectrum, we prove at the same time orbital and asymptotic stability. We are not able to get the full result proved by Cuccagna for the nonlinear Schrodinger equation, because of the strong indefiniteness of the energy.
We study the behavior of perturbations of small nonlinear Dirac standing waves. We assume that the linear Dirac operator of reference $H=D_m+V$ has only two double eigenvalues and that degeneracies are due to a symmetry of $H$ (theorem of Kramers). I
Continuing a line of investigation initiated in [11] exploring the connections between Jost and Evans functions and (modified) Fredholm determinants of Birman-Schwinger type integral operators, we here examine the stability index, or sign of the firs
In this paper we deal with two dimensional cubic Dirac equations appearing as effective model in gapped honeycomb structures. We give a formal derivation starting from cubic Schrodinger equations and prove the existence of standing waves bifurcating from one band-edge of the linear spectrum.
We prove the existence of infinitely many non square-integrable stationary solutions for a family of massless Dirac equations in 2D. They appear as effective equations in two dimensional honeycomb structures. We give a direct existence proof thanks t
We study bifurcations and spectral stability of solitary waves in coupled nonlinear Schrodinger equations (CNLS) on the line. We assume that the coupled equations possess a solution of which one component is identically zero, and call it a $textit{fu