Abstract
The linear stability of planar solitary waves with respect to long-wavelength transverse perturbations is studied in the framework of the generalized Kadomtsev-Petviashvili equation. It is newly discovered that for some nonlinearities in this family, the solitary waves could be transversely unstable even in a medium with negative dispersion. In the case of positive dispersion, they are found to be always unstable.
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