236 research outputs found
Finite-time blowup for a complex Ginzburg-Landau equation with linear driving
In this paper, we consider the complex Ginzburg--Landau equation on , where
, and . By convexity
arguments we prove that, under certain conditions on ,
a class of solutions with negative initial energy blows up in finite time
Convergence of numerical schemes for short wave long wave interaction equations
We consider the numerical approximation of a system of partial differential
equations involving a nonlinear Schr\"odinger equation coupled with a
hyperbolic conservation law. This system arises in models for the interaction
of short and long waves. Using the compensated compactness method, we prove
convergence of approximate solutions generated by semi-discrete finite volume
type methods towards the unique entropy solution of the Cauchy problem. Some
numerical examples are presented.Comment: 31 pages, 7 figure
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