A weak nonlinear plant can be linearized and will track an input signal if the plant is preceded by a nonlinear controller which approximates the inverse of the plant’s transfer function. Present techniques for adjusting the controller adaptively to the plant require an additional nonlinear adaptive filter to perform a separate system identification. Straightforward update algorithms can not di...

1. INTRODUCTION As the level of detail and intricacy of dynamical system models continues to grow, the essential behaviour of such systems can be lost in a cloud of complexity. Furthermore, numerical simulations of such systems can consume extensive memory resources and take inordinate amounts of time. Consequently, to cope with the growing complexity and dimension-ality of systems, model reduc...

Weakly nonlinear oscillations exhibit a wide range of phenomena not seen in simple linear oscillations. This paper considers weakly nonlinear oscillations with an analytic forcing term, and attempts to understand various quantitative solution methods for this problem. We give a quantitative demonstration of the failure of regular perturbation theory, and use this failure to motivate investigati...

In inviscid fluid flows instability arises generically due to a resonance between two wave modes. Here, it is shown that the structure of the weakly nonlinear régime depends crucially on whether the modal structure coincides, or remains distinct, at the resonance point where the wave phase speeds coincide. Then in the weakly nonlinear, long-wave limit the generic model consists either of a Bous...

An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems. We consider the resonance conditions for some classes of solutions. The averaged system can be solved numerically in the resonance case. The shallow water pr...

We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schrödinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB–analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.

In this paper, we first construct a preconditioned two-parameter generalized Hermitian and skew-Hermitian splitting (PTGHSS) iteration method based on the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method for non-Hermitian positive definite linear systems. Then a class of PTGHSSbased iteration methods are proposed for solving weakly nonlinear systems base...

We predict theoretically and numerically the existence of incoherent dispersive shock waves. They manifest themselves as an unstable singular behavior of the spectrum of incoherent waves that evolve in a noninstantaneous nonlinear environment. This phenomenon of "spectral wave breaking" develops in the weakly nonlinear regime of the random wave. We elaborate a general theoretical formulation of...

In this paper we deal with a model of coupled non-stationary electroelasticity with displacements and potential given on the boundary of a body. We construct a numerical scheme for modeling electromechanical interactions in the body, and present a spectrum of a priori estimates for the solution of this scheme. Such estimates allow us to prove the convergence of the scheme to a generalized solut...

In this paper the operator-diierence scheme for the numerical solution of a problem arising from coupled eld theory is thoroughly investigated for the case when the classical assumptions of suucient smoothness cannot be applied. Such a situation, being typical in many applications, is considered for the problem of nonstationary electroelasticity. A new a-priori estimation for the numerical solu...