We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation techniques, obtaining a full range of power-like decay rates. In particular, we give explicit estimates with respect to the initial data. We discuss several ...

A simple derivation of the general equations of the Tamm-Dankoff approximation (TDA) is presented using the equation-of-motion technique to describe electronic excitations in molecules. It is emphasized that the performance of this method strongly depends on the accuracy of the reference (ground) state. Though the HartreeFock ground state is commonly applied, the 'all-single CI' (CIS) method ba...

In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation with both second-order and fourth-order wave terms, which is extended from the classical beam equation arising in the historical events of travelling wave behavior in the Golden Gate Bridge in San Francisco. We perform a complete Lie symmetry group classification by using the equivalence transformation group ...

This article studies almost global existence for solutions of quadratically quasilinear systems of wave equations in three space dimensions. The approach here uses only the classical invariance of the wave operator under translations, spatial rotations, and scaling. Using these techniques we can handle wave equations in Minkowski space or Dirichletwave equations in the exterior of a smooth, sta...

The Korteweg-de Vries (KdV) equation is known as a model of long waves in an infinitely long canal over a flat bottom and approximates the two-dimensional water wave problem, which is a free boundary problem for incompressible Euler equation with the irrotational condition. In this paper, we consider the validity of this approximation in the case of presence of surface tension. Moreover, we con...

In the theoretical investigation, directly seeking exact solutions for nonlinear partial differential equations has become one of the central themes of perpetual interest in mathematical physics. Nonlinear wave phenomena appear in many fields, such as fluid mechanics, biomathematics, plasma physics, optical fibers, chemical physics, and other areas of engineering. These nonlinear phenomena are ...

We explore Yang’s Noncommutative space-time algebra (involving two length scales) within the context of QM defined in Noncommutative spacetimes; the Holographic principle and the area-coordinates algebra in Clifford spaces. Casimir invariant wave equations corresponding to Noncommutative coordinates and momenta in d-dimensions can be recast in terms of ordinary QM wave equations in d + 2-dimens...