Stability of Solitary Waves of the Kadomtsev-Petviashvili Equation with a Weak Rotation

We consider the stability of solitary wave solutions of the rotation-generalized Kadomtsev--Petviashvili (RGKP) equation. Using an iteration method developed by Petviashvili, we numerically compute the solitary waves over a range of the parameters $c$ and $\gamma$ and use these to determine the concavity of the function $d(c)$ that determines their stability. In spite of the absence of any scaling invariance property for the RGKP equation, we prove the strong instability of the solitary waves.

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