Weakly nonlinear oscillations exhibit a wide range of phenomena not seen in simple linear oscillations. This paper considers weakly nonlinear oscillations with an analytic forcing term, and attempts to understand various quantitative solution methods for this problem. We give a quantitative demonstration of the failure of regular perturbation theory, and use this failure to motivate investigati...

We show that the well-known binomial states and negative binomial states of the radiation field and their excitations are nonlinear coherent states.Excited nonlinear coherent state are still nonlinear coherent states with different nonlinear functions.We finally give exponential form of the nonlinear coherent states. PACS numbers:42.50.Dv,03.65.Db,32.80.Pj,42.50.Vk Typeset using REVTEX ∗email:x...

Current generalizations of the classical Einstein–Hilbert Lagrangian formulation of General Relativity are reviewed. Some alternative variational principles, based on different choices of the gravitational field variable (metric tensor, affine connection, or both) are known to reproduce – more or less directly – Einstein’s gravitational equations, and should therefore be regarded as equivalent ...

We describe a relatively simple time-dependent convection model that can be coupled to the equations of radiation hydrodynamics. We show that it behaves in a physically plausible way in protostellar collapse flows and is quantitatively correct for nonlinear RR-Lyrae pulsations and the Sun. Together with the equations of radiation hydrodynamics the model closely approximates the classical stella...

The existence and uniqueness of the state trajectories (limiting substrate and living biomass) are analyzed for a tubular biochemical reactor nonlinear model. It is mainly reported that the trajectories exist on the whole (nonnegative real) time axis and the set of all physically feasible state values is invariant under the dynamics equations. This set takes into account the positivity of the s...

We report on two microfluidic elastomeric autoregulatory devices-a diode and a rectifier. They exhibit physically interesting and complex nonlinear behaviors (saturation, bias-dependent resistance, and rectification) with a Newtonian fluid. Due to their autoregulatory properties, they operate without active external control. As a result, they enable increased microfluidic device density and ove...

This paper applies He’s variational iteration method for solving two systems of Volterra integro-differential equations. The solution process is illustrated and various physically relevant results are obtained. Comparison of the obtained results with exact solutions shows that the used method is an effective and highly promising method for various classes of both linear and nonlinear integro-di...

The primitive equations (PEs) of the atmosphere and the oceans without viscosity are considered. These equations are not well-posed for any set of local boundary conditions. In space dimension 2.5 a set of nonlocal boundary conditions has been proposed in [4]. The present article is aimed at testing the validity of these boundary conditions with physically relevant data. The issues tested are t...

The possibility of physically relevant singular solutions of the nonlinear Schrodinger equation (NLSE) with sustained dissipation into the singularity is considered through numerical study of a dissipative regularisation and its small dissipation limit. A new form of such dissipative solutions is conjectured for certain parameter ranges where this behaviour was previously not expected, involvi...

Lévy flight models are often used to describe stochastic processes in complex systems. However, due to the occurrence of diverging position and/or velocity fluctuations Lévy flights are physically problematic if describing the dynamics of a particle of finite mass. Here we show that the velocity distribution of a random walker subject to Lévy noise can be regularized by nonlinear friction, lead...