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The KdV equation can be considered as a special case of the general equationutCf .u/x−g.uxx/x D 0;> 0;wheref is non-linear andg is linear, namelyf .u/ D u2=2 andg.v/ D v. As the parameter  t...
Consider a point mass falling vertically on an innitely heavy horizontal plate which oscillates periodically with period 2π in the vertical direction and interacts with the particle by the l...
In this paper we describe the long time behavior of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of the corresponding di@...
A model of a strip of cardiac tissue consisting of a one-dimensional chain of cardiac units is derived in the form of a non-linear partial difference equation. Perturbation analysis is performed on th...
We consider the CDMA (code-division multipleaccess) multi-user detection problem for binary signals and additive white gaussian noise. We propose a spreading sequences scheme based on random sparse si...
We give an expository survey on the subject of the Yamabe-type problem and applications. With a recent technique in hand, we also present a simplified proof of the result by Chang-Gursky-Yang on...
Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering f...
In this short letter we show that the one dimensional non linear Schr¨odinger equation(NLS)can be solved by a Hopf-Cole transformation which converts it to the Burgers equation in turbulence.
This paper is concerned with H¨older regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we ass...
We consider propagation of optical pulses under the interplay of dispersion and Kerr non-linearity in optical fibres with impurities distributed at random uniformly on the fibre. By using a model base...
We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-cha...

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