We formulate a multi-scale perturbation technique to asymptotically solve weakly nonlinear hyperbolic equations. The method is based on a set of scaled characteristic coordinates. We show that this technique leads to a simplified system of ordinary differential equations describing the weakly nonlinear interaction between left and right running waves. Using this method, a uniformly valid first ...

In this paper a coupled problem of dynamic electroelasticity is investigated using the variational approach and the concept of generalized solutions. We derive a numerical procedure directly from the deenition of the generalized solution of the problem. We prove the convergence of the numerical scheme (with the second order in space-time) to the solution of the original problem from a class of ...

– We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order parameter, or a concentration profile. We show that two types of dynamics occur around the transition: weakly nonlinear dynamics, or highly nonlinear dynamics. Th...

A short review of the theory of weakly nonlinear water waves, prepared for the forthcoming Encyclopedia of Nonlinear Science

The main object of this paper is to study the weakly nonlinear hydrodynamic stability of the thin Newtonian fluid flowing on a rotating circular disk. A long-wave perturbation method is used to derive the nonlinear evolution equation for the film flow. The linear behaviors of the spreading wave are investigated by normal mode approach, and its weakly nonlinear behaviors are explored by the meth...

using nonlinear mathematical analysis, on the data obtained for.time seriesof shahd-iran price during 3.5 years, the characteristics,of the process associated with this, is analysed. analysing the behaviour of the time series associated with returns is indicative ofits short-term predictability nature. however, employing analysis regarding the correlation dimension estimate. it is indicated tha...

Free surface potential flows past disturbances in a channel are considered. Three different types of disturbance are studied: (i) a submerged obstacle on the bottom of a channel; (ii) a pressure distribution on the free surface; and (iii) an obstruction in the free surface (e.g. a sluice gate or a flat plate). Surface tension is neglected, but gravity is included in the dynamic boundary conditi...

Instabilities of a thin viscous film flowing down a uniformly heated plane are investigated in this study. The heating generates a surface tension gradient that induces thermocapillary stresses on the free surface. Thus, the film is not only influenced by gravity and mean surface tension but also the thermocapillary force is acting on the free surface. Moreover, the heat transfer at the free su...