Blowup and ill-posedness for the complex, periodic KdV equation
Résumé
This paper is concerned with complex-valued solutions of the Korteweg–de Vries equation. Interest will be focused upon the initial-value problem with initial data that is periodic in space. Derived here are results of local and global well-posedness, singularity formation in finite time and, perhaps surprisingly, results of non-existence. The overall picture is notably different from the situation that obtains for real-valued solutions.
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