An invariant set bifurcation theory for nonautonomous nonlinear evolution equations

Integrable Nonautonomous Nonlinear Schrödinger Equations

We show that a recently given nonautonomous nonlinear Schrodinger equation (NLSE) can be transformed into the autonomous NLSE.

Maximal regularity for nonautonomous evolution equations

We derive sufficient conditions, perturbation theorems in particular, for nonautonomous evolution equations to possess the property of maximal Lp regularity. 1991 Mathematics Subject Classification. 35K90, 47D06.

Asymptotic Behaviour of Parabolic Nonautonomous Evolution Equations

Effects of the Bogie and Body Inertia on the Nonlinear Wheel-set Hunting Recognized by the Hopf Bifurcation Theory

Nonlinear hunting speeds of railway vehicles running on a tangent track are analytically obtained using Hopf bifurcation theory in this paper. The railway vehicle model consists of nonlinear primary yaw dampers, nonlinear flange contact stiffness as well as the clearance between the wheel flange and rail tread. Linear and nonlinear critical speeds are obtained using Bogoliubov method. A compreh...

Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations

Abstract: In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspace...