The bi-Hamiltonian structure of the two known vector generalizations of the mKdV hierarchy of soliton equations is derived in a geometrical fashion from flows of nonstretching curves in Riemannian symmetric spaces G/SO(N). These spaces are exhausted by the Lie groups G = SO(N + 1), SU(N). The derivation of the bi-Hamiltonian structure uses a parallel frame and connection along the curve, tied t...

We consider a coupled PDE system arising in noise reduction problems. In a two dimensional chamber, the acoustic pressure (unwanted noise) is represented by a hyperbolic wave equation. The floor of the chamber is subject to the action of piezo-ceramic patches (smart materials). The goal is to reduce the acoustic pressure by means of the vibrations of the floor which is modelled by a hyperbolic ...

This paper presents the perturbation theory for the double–sine–Gordon equation. We received the system of differential equations that shows the soliton parameters modification under perturbation’s influence. In particular case λ = 0 the results of the research transform into well-known perturbation theory for the sine–Gordon equation.

We describe and characterize rigorously the homoclinic structure of the perturbed sine{ Gordon equation under periodic boundary conditions. The existence of invariant manifolds for a perturbed sine{Gordon equation is established. Mel'nikov method, together with geometric analysis are used to assess the persistence of the homoclinic orbits under bounded and time-periodic perturbations.

in this paper, the chebyshev spectral collocation method(cscm) for one-dimensional linear hyperbolic telegraph equation is presented. chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. a straightforward implementation of these methods involves the use of spectral differentiation matrices. firstly, we transform ...

In this paper, the authors provide several sharp upper and lower bounds for Neuman–Sándor mean in terms of arithmetic contra-harmonic means, present some new inequalities involving hyperbolic sine function cosine function.

Compression tests of a Mg-13Gd-4Y-2Zn-0.5Zr alloy were carried out on Gleeble-1500D thermo-mechanical simulator within temperature range 420–500 °C and strain rate 0.001–5 s–1 so that the corresponding flow behavior was investigated. The Zener-Hollomon parameter Z used in hyperbolic-sine-type equation to express relationships between peak stress, deformation rate. Work hardening, dynamic recove...