| Abstract: |
| We consider the exact solutions of the generalized Constantin-Lax-Majda equation with dissipation $-\Lambda^\sigma$, where $\widehat {{\Lambda}^\sigma}=|k|^\sigma$, both for the problem on the circle $x \in [-\pi,\pi]$ and the real line. We analyze these solutions from the stand point of complex pole singularities and their motion in the complex space and find conditions for collapse in these solutions in a finite time for various advection parameter, dissipation coefficient and $\sigma$ values. |
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