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The equation with $\\al=0$ was first introduced by G{\\'e}rard and Grellier in \\cite{GG1} as a toy model for totally non dispersive evolution equations. We establish the following properties for this equation. For $\\al\\textless{}0$, any compact subset of initial data leads to a relatively compact subset of trajectories. 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The equation with $\\al=0$ was first introduced by G{\\'e}rard and Grellier in \\cite{GG1} as a toy model for totally non dispersive evolution equations. We establish the following properties for this equation. For $\\al\\textless{}0$, any compact subset of initial data leads to a relatively compact subset of trajectories. 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