| Abstract: |
| We consider the quasi-linear Hamiltonian mKdV equation $\varphi_t+\partial_x^3\varphi+\partial_x (\varphi^3)+\partial_x[c(\varphi)\partial_x(c(\varphi)\partial_x\varphi)]=0$. We prove that when the initial data is sufficiently smooth, localized and small, the solution exists global-in-time. |
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