We apply a multiple–time version of the reductive perturbation method to study long waves as governed by the Boussinesq model equation. By requiring the absence of secular producing terms in each order of the perturbative scheme, we show that the solitary–wave of the Boussinesq equation can be written as a solitary–wave satisfying simultaneously all equations of the KdV hierarchy, each one in a...

The trajectory-tracking control of a typical industrial robot with six revolute joints is studied, where the joint flexibility is taken into account. An explicit form of the control law is obtained by using the composite control technique. The stability of system is discussed. The global convergence of tracking error can be reached by tuning the controller parameters. This method has a unique a...

The Residual–Free Bubble Method for Problems with Multiple Scales Andrea Cangiani St Hugh’s College Doctor of Philosophy Trinity Term 2004 This thesis is devoted to the numerical analysis and development of the residual–free bubble finite element method. We begin with an overview of known results and properties of the method, showing how techniques used on a range of multiscale problems can be ...

An alternative example of the method of multiple scales is presented. This example arises in the study of the classical heat equation with a slowly varying flux imposed at one end. The module presents introductory ideas about dimensionless variables, multiple-scale expansions, and scaling of the dependent variable. The necessarily obfuscating algebraic computation is less than that for more fam...

Terrestrial vegetation influences climate by modifying the radiative-, momentum-, and hydrologicbalance. This paper contributes to the ongoing debate on the question whether positive biogeophysical feedbacks between vegetation and climate may lead to multiple equilibria in vegetation and climate and consequent abrupt regime shifts. Several modelling studies argue that vegetation-climate feedbac...

in this paper, first a new homotopy perturbation method for solving a fractional order nonlinear telegraph equation is introduced. by applying the proposed method, the nonlinear equation is translated to linear equations for per iteration of homotopy perturbation method. then, the obtained problems are solved with separation method. in the examples, it is illustrated that the exact solution is ...

Abstract This paper investigates the transverse 3:1 internal resonance of an axially transporting nonlinear viscoelastic Euler-Bernoulli beam with a two-frequency parametric excitation caused by speed perturbation. The Kelvin-Voigt model is introduced to describe characteristics beam. governing equation and associated boundary conditions are obtained Newton’s second law. method multiple scales ...

We compute the non-Gaussianity of the curvature perturbation generated by ekpyrotic collapse with multiple fields. The transition from the multi-field scaling solution to a single-field dominated regime converts initial isocurvature field perturbations to an almost scale-invariant comoving curvature perturbation. In the specific model of two fields, φ1 and φ2, with exponential potentials, −Vi e...

We prove the existence and uniqueness of solutions of weakly non-linear wave equations in the region x > 0; t > 0 under arbitrary initial and boundary conditions. We also establish the asymptotic validity of formal perturbation approximations to the solutions. The asymptotics of these equations require two slow scales, one spatial, one temporal. We formulate a multiple-scale perturbation proced...

in this paper, the homotopy perturbation method (hpm) and elzaki transform is employed to obtain the approximate analytical solution of the sine gorden and the klein gorden equations. the nonlinear terms can be handled by the use of homotopy perturbation method. the proposed homotopy perturbation method is applied to reformulate the first and the second order initial value problems which leads ...