41 citations · 179 across the 30 of their papers we have counts for
23 papers · 1 filter
Stable bi-frequency spinor modes as Dark Matter candidates
Andrew Comech, Niranjana Kulkarni, Nabile Boussaïd +1
We show that spinor systems with scalar self-interaction, such as the Dirac--Klein--Gordon system with Yukawa coupling or the Soler model, generically have bi-frequency solitary wa…
On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D
Nabile Boussaïd, Andrew Comech, Niranjana Kulkarni
For the nonlinear Dirac equation with scalar self-interaction (the Soler model) in three spatial dimensions, we consider the linearization at solitary wave solutions and find the i…
Attractors of Hamiltonian nonlinear partial differential equations
Andrew Comech, Alexander Komech, Elena Kopylova
We survey the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. These are results on global attraction to stationary states…
On solutions with compact spectrum to nonlinear Klein--Gordon and Schroedinger equations
Andrew Comech
We consider finite energy solutions to the nonlinear Schroedinger equation and nonlinear Klein--Gordon equation and find the condition on the nonlinearity so that the standard, one…
Virtual levels and virtual states of linear operators in Banach spaces. Applications to Schroedinger operators
Nabile Boussaid, Andrew Comech
We develop a general approach to virtual levels in Banach spaces. We show that virtual levels admit several characterizations which are essentially equivalent: (1) there are corres…
On spectral and orbital stability for the Klein--Gordon equation coupled to an anharmonic oscillator
Andrew Comech, Elena A. Kopylova
We obtain explicit characterization of spectral and orbital stability of solitary wave solutions to the -invariant Klein--Gordon equation in one spatial dimension co…