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We present the results of a large number of careful numerical experiments carried out to investigate the way that the solution of the integrable focusing nonlinear Schrodinger equation with - xed ini...
In this paper we characterize a dyadic type Besov space as an adequate setting to solve the Schr\"{o}dinger-Dirac type equation $i\tfrac{\partial u}{\partial t}=D^{\beta}u$ with $u(x,0)=u^0$ pointwise...
In this paper, we consider in R^n the Cauchy problem for nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2. It is well known that this problem is ill posed. However, We...
The small dispersion limit of the focusing nonlinear Schro\"odinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales....
The Einstein equations in wave map gauge are a geometric second order system for a Lorentzian metric. To study existence of solutions of this hyperbolic quasi diagonal system with initial data on a ch...
In this paper we investigate the regularizing behavior of two-phase Stefan problem near initial data. The main step in the analysis is to establish that in any given scale, the scaled solution is very...
In a recent paper, Kiessling and Tahvildar-Zadeh proved that any spherically symmetric classical solution of the attractive relativistic Vlasov-Poisson equation launched by sufficiently regular initi...
For s > 3=2 two sequences of CH solutions living in a bounded set of the Sobolev space Hs(R) are constructed, whose distance at the initial time is converging to zero while at any later time is bounde...
We study the Cauchy initial-value problem for the Benjamin-Ono equation in the zero-disperion limit, and we establish the existence of this limit in a certain weak sense by developing an appropriate a...
We study the (n+1)-dimensional generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation, a universal equation describing the propagation of weakly nonlinear, quasi one dimensional wa...
In this paper we investigate the life-span of classical solutions to the hyperbolic geometric °ow in two space variables with slow decay initial data. By establishing some new estimates on the solutio...
In this paper, we first give a lower bound of the lifespan and some estimates of classical solutions to the Cauchy problem for general quasi-linear hyperbolic systems, whose characteristic fields are ...
In this paper we study solvability of the Cauchy problem of the Kawahara equation $\partial_tu+au\partial_xu+\beta\partial^3_xu+\gamma\partial^5_xu =0$ with $L^2$ initial data. By working on the Bourg...
The Cauchy problem for the equation \begin{equation} Mw\equiv \sumj=0m\sums=0ljas,j\frac{\partials+jw(z1,z2)}{\partial z1s\partial z2j}=0 \end{equation} \begin{equation} \frac{\partialnw(z1,z2)}{\part...

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