We study the spectral properties of the linearized Eu-ler operator obtained by linearizing the equations of incompress-ible two dimensional fluid at a steady state with the vorticity that containsâ€¦ (More)

The question for linear stability of spatially periodic waves for the Boussinesq equation (the cases p = 2, 3) and the Klein-Gordon-Zakharov system are considered. For a wide class of solutions, weâ€¦ (More)

We study traveling waves Ï†c of second order in time PDEâ€™s utt + Lu + N(u) = 0. The linear stability analysis for these models is reduced to the question for stability of quadratic pencils in the formâ€¦ (More)

We study the asymptotic behavior of the solutions of the Benjamin-BonaMahony equation defined on R3. We first provide a sufficient condition to verify the asymptotic compactness of an evolutionâ€¦ (More)

We present a new necessary and sufficient condition to verify the asymptotic compactness of an evolution equation defined in an unbounded domain, which involves the Littlewood-Paley projectionâ€¦ (More)

We consider the viscous Camassa-Holm equation subject to an external force, where the viscosity term is given by second order differential operator in divergence form. We show that under some mildâ€¦ (More)

We develop a general theory to treat the linear stability of certain special solutions of second order in time evolutionary PDE. We apply these results to standing waves of the following problems:â€¦ (More)

We consider the quadratic and cubic KP I and NLS models in 1+2 dimensions with periodic boundary conditions. We show that the spatially periodic travelling waves (with period K) in the form u(t, x,â€¦ (More)

We consider the Camassa-Holm equation with data in the energy norm H 1(R1). Global solutions are constructed by the small viscosity method for the frequency localized equations. The solutions areâ€¦ (More)

We consider positive, radial and exponentially decaying steady state solutions of the general reactionâ€“diffusion and Kleinâ€“Gordon type equations and present an explicit construction ofâ€¦ (More)