The evolution along a tank of unidirectional nonlinear wave groups with narrow spectrum previously studied in [1] is compared with numerical simulations based on weakly, strongly and fully nonlinear models. Measurements of the instantaneous surface elevation within the laboratory tank were carried out using digital processing of video-recorded sequences of images of the contact line movement at...

Keywords: Schauder fixed point principle Exponentially stable Acquistapace–Terreni conditions Evolution families Almost periodic Higher-order differential equation with operator coefficients Wave equation with fractional damping a b s t r a c t In this paper, we make extensive use of the well-known Schauder fixed point principle and the exponential stability of the evolution family involved to ...

The tanh method is a powerful solution method; various extension forms of the tanh method have been developed with a computerized symbolic computation and is used for constructing the exact travelling wave solutions, of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. First a power series in tanh was used as an ansatz t...

A fast and stable method is formulated to compute the time evolution of a wave function by numerically solving the time-dependent Schrodinger equation. This method is a real-space-real-time evolution method implemented by several computational techniques such as Suzuki's exponential product, Cayley's form, the finite differential method, and an operator named adhesive operator. This method cons...

The tanh method is a powerful solution method; various extension forms of the tanh method have been developed with a computerized symbolic computation and is used for constructing the exact travelling wave solutions, of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. First a power series in tanh was used as an ansatz t...

The time evolution of a two-level atom which is simultaneously exposed to the field of a running laser wave and a homogeneous gravitational field is studied. The result of the coupled dynamics of internal transitions and center-of-mass motion is worked out exactly. Neglecting spontaneous emission and performing the rotating wave approximation we derive the complete time evolution operator in an...

An experimental study of hydrodynamic perturbation evolution in a strong unsupported shock wave, which is immediately followed by an expansion wave, is reported. A planar solid plastic target rippled on the front side is irradiated with a 350-450 ps long laser pulse. The perturbation evolution in the target is observed using face-on monochromatic x-ray radiography during and for up to 4 ns afte...

We study the formation, evolution and structure of dissipative fronts produced by overtaking collisions of relativistic streams, with emphasis on strongly magnetized flows. The evolution of the system is followed using analytical approach in the simple wave regime and numerical simulations in the non-simple wave regime, until a steady-state is reached. The steady-state structure of the front is...

We investigate the nonlinear dynamics underlying the evolution of a 2-D ferromagnetic film with uniaxial anisotropy and an oscillating magnetic field. Considering the associated Landau-Lifshitz spin evolution equation with Gilbert damping included, we study the dynamics in terms of the stereographic variable. We identify several new fixed points for suitable choice of external field. In particu...

An optimum design technique for balanced surface acoustic wave (SAW) filters is proposed. First of all, in order to evaluate the performance of balanced SAW filters by the computer simulation, a numerical model of balanced SAW filters is derived by using mixed-mode scattering parameters. Then the structural design of balanced SAW filters is formulated as a function optimization problem that aim...