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Applied
Math Seminar |
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The possibility of blowup in the Nonlinear Schrodinger
equation (NLS) was predicted theoretically and observed numerically in
1965. Until now, however, there has been no systematic study of what exactly
happens when/after finite-difference methods `break down' near the singularity.
Thus, for example, the consequences of using second-order discretization
versus fourth-order one have not been analyzed. In this talk we present
some recent results on discretization effects in blowup solutions of NLS
equations. As we shall see, analysis of discretization effects leads to
modified equations which are NLS with high-order anisotropic dispersion.
Therefore, part of this talk will be devoted to recent results on the
general theory of NLS with high-order dispersion. |