Local well-posedness for the Sixth-Order Boussinesq Equation

This work studies the local well-posedness of the initial-value problem for the nonlinear sixth-order Boussinesq equation $u_{tt}=u_{xx}+βu_{xxxx}+u_{xxxxxx}+(u^2)_{xx}$, where $β=\pm1$. We prove local well-posedness with initial data in non-homogeneous Sobolev spaces $H^s(\R)$ for negative indices of $s \in \R$.

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