We construct non-Abelian analogs for some KdV type equations, including the (rational form of) exponential Calogero--Degasperis equation and generalizations of Schwarzian equation. Equations differential substitutions under study contain arbitrary parameters.

Keywords: Delay equations Exponential stability Oscillating coefficient Bohl–Perron type theorem a b s t r a c t New explicit exponential stability conditions are obtained for the nonautonomous linear equation ˙ x(t) + a(t)x(h(t)) = 0, where h(t) ≤ t and a(t) is an oscillating function. We apply the comparison method based on the Bohl–Perron type theorem. Coefficients and delays are not assumed...

I calculate the hydrodynamic limit of the BGK approximation of the Boltzmann equation for the case of a long stress relaxation time and find that the stress obeys a viscoelastic constitutive equation. The constitutive equation is different from standard constitutive equations used for polymeric liquids in that it is not “objective” because inertial effects are important. I calculate the exact s...

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with acoustic boundary in a bounded domain in Rn. To stabilize the system, we incorporate separately, the passive viscous damping in the model as like Gannesh C. Gorain [1]. Energy decay rate is obtained by the exponential stability of solutions by using multiplier technique.

We review recent results concerning the exponential behaviour of transition probabilities across a gap in the adiabatic limit of the time-dependent Schrödinger equation. They range from an exponential estimate in quite general situations to asymptotic Landau-Zener type formulae for finite dimensional systems, or systems reducible to this case.