In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differ...

There have been many attempts [I-31 to produce correct pomeron by putting the nparticle production amplitude expht, in the unitarity integral equation. It was found that for reasonable values of h one could not get the right picture of the slope of the pomeron as a function of energy S4 .W e show that theinterference termsin the unitary equation does not improve the slope either. However, a...

After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation. Regarding nonhyperbolic transitions we discuss a four-dimensional relaxation oscillation and also canard-like solutions emerging from the mo...

consider the following consistent sylvester tensor equation[mathscr{x}times_1 a +mathscr{x}times_2 b+mathscr{x}times_3 c=mathscr{d},]where the matrices $a,b, c$ and the tensor $mathscr{d}$ are given and $mathscr{x}$ is the unknown tensor. the current paper concerns with examining a simple and neat framework for accelerating the speed of convergence of the gradient-based iterative algorithm and ...

We develop the inverse scattering transform method for the Novikov equation ut − utxx + 4uux = 3uuxuxx + uuxxx considered on the line x ∈ (−∞,∞) in the case of non-zero constant background. The approach is based on the analysis of an associated Riemann–Hilbert (RH) problem, which in this case is a 3×3 matrix problem. The structure of this RH problem shares many common features with the case of ...

A Dispersive Wave Equation in 2 + 1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and techniques based upon the Painlevé Property leading to the Double Singular Manifold Expansion we shall find the Miura Transformation which converts the 2LDW Equation into the...

This paper considers the backward error analysis of stochastic differential equations (SDEs), a technique that has been of great success in interpreting numerical methods for ODEs. It is possible to fit an ODE (the so called modified equation) to a numerical method to very high order accuracy. Backward error analysis has been particularly valuable for Hamiltonian systems, where symplectic numer...

We prove that a class of A-stable symplectic Runge–Kutta time semidiscretizations (including the Gauss–Legendre methods) applied to a class of semilinear Hamiltonian PDEs which are well-posed on spaces of analytic functions with analytic initial data can be embedded into a modified Hamiltonian flow up to an exponentially small error. As a consequence, such timesemidiscretizations conserve the m...