Nonlinear dispersive wave equations arise naturally in scientific and engineering fields such as fluid dynamics, electromagnetic theory, quantum mechanics, optical communication, nonlinear optics etc. Many important questions (both in theory and applications) are related to the interaction of two effects: energy spreading (dispersion, diffraction) and energy concentrating (nonlinear self-trappi...

Cooker’s sloshing experiment is a prototype for studying the dynamic coupling between fluid sloshing and vessel motion. It involves a container, partially filled with fluid, suspended by two cables and constrained to remain horizontal while undergoing a pendulum-like motion. In this paper the fully-nonlinear equations are taken as a starting point, including a new derivation of the coupled equa...

the control of fluidized-bed operations processes is still one of the major areas of research due to the complexity of the process and the inherent nonlinearity and varying dynamics involved in its operation. there are varieties of problems in chemical engineering that can be formulated as nonlinear programming (nlps). the quality of the developed solution significantly affects the performance ...

Extending previous work with Lattanzio and Mascia on the scalar (in fluid-dynamical variables) Hamer model for a radiative gas, we show nonlinear orbital asymptotic stability of smallamplitude shock profiles of general systems of coupled hyperbolic–eliptic equations of the type modeling a radiative gas, that is, systems of conservation laws coupled with an elliptic equation for the radiation fl...

Article history: Received 7 February 2012 Available online 13 August 2012 We derive and justify a normal form reduction of the nonlinear Schrödinger equation for a general pitchfork bifurcation of the symmetric bound state that occurs in a double-well symmetric potential. We prove persistence of normal form dynamics for both supercritical and subcritical pitchfork bifurcations in the timedepend...

Wave group dynamics is studied in the framework of the extended Korteweg-de Vries equation. The nonlinear Schrodinger equation is derived for weakly nonlinear wave packets, and the condition for modulational instability is obtained. It is shown that wave packets are unstable only for a positive sign of the coe cient of the cubic nonlinear term in the extended Korteweg-de Vries equation, and for...

The transport equation, in highly scattering regimes, has a limit in which the dominant behavior is given by the solution of a di usion equation. Angular discretization like the discrete ordinate method (SN ), the truncated spherical harmonic expansion (PN ) or also nonlinear moment models have the same property. For such systems it would be interesting to construct nite volume schemes on unstr...

This Letter describes the theoretical structure of the plasma diffusion layer that develops from an initially sharp gas-metal interface. The layer dynamics under isothermal and isobaric conditions is considered so that only mass diffusion (mixing) processes can occur. The layer develops a distinctive structure with asymmetric and highly nonlinear features. On the gas side of the layer the diffu...

tension-leg platform (tlp) is a vertically moored floating structure. the platform is permanently mooredby tendons. surge equation of motion of tlp is highly nonlinear because of large displacement and it should be solved with perturbation parameter in time domain. this paper compare the dynamic motion responses of a tlp in regular sea waves obtained by applying three method in time domain usin...

We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain are integrable equations. They generalize known nonlinear differential equations for correlation functions at equilibrium [1, 2, 3, 4] and provide vital tools...