Near-wall turbulence in the buffer region is qualitatively characterized in terms of recentlyfound nonlinear three-dimensional solutions to the incompressible Navier–Stokes equation for wall-bounded shear flows. Jiménez & Simens’ (2001) traveling-wave solution for an autonomous wall flow, Nagata’s (1990) steady and Kawahara & Kida’s (2001) periodic solutions for a plane Couette flow are conside...

We first briefly survey the recent results for existence of solutions to first-order problems with fixed-time impulses. Periodic boundary conditions using upper and lower solutions were considered in [19], using degree theory. A nonlinear alternative of Leray-Schauder type was used in [15] for initial conditions or periodic boundary conditions. The monotone iterative technique was employed in [...

We present a new numerical method for the efficient computation of periodic solutions of nonlinear systems of Delay Differential Equations (DDEs) with several discrete delays. This method exploits the typical spectral properties of the monodromy matrix of a DDE and allows effective computation of the dominant Floquet multipliers to determine the stability of a periodic solution. We show that th...

There has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. The popular Poincare-Bendixon theorem applies well to the former but not the latter (see [2] and [3]). We give a necessary condition for the existence of periodic solutions for the third order autonomous system...

A new computational scheme using Chebyshev polynomials is proposed for the numerical solution of parametrically excited nonlinear systems. The state vector and the periodic coefficients are expanded in Chebyshev polynomials and an integral equation suitable for a Picard-type iteration is formulated. A Chebyshev collocation is applied to the integral with the nonlinearities reducing the problem ...

Abstract. We present a second order accurate numerical scheme for a nonlinear hyperbolic equation with an exponential nonlinear term. The solution to such an equation is proven to have a conservative nonlinear energy. Due to the special nature of the nonlinear term, the positivity is proven to be preserved under a periodic boundary condition for the solution. For the numerical scheme, a highly ...

Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic balance (HB) method its variants have been the most widely-used approaches for such systems, but are either confined to low-order approximations or impaired by aliasing improper-sampling problems. Here we propose a collocation-based framework successfully unify reconstruct HB-like methods. Under this new cond...