Title: Smooth positon solutions of the focusing modified Korteweg-de Vries equation,
Abstract: The $n$-fold Darboux transformation $T_{n}$ of the focusing real mo\-di\-fied
Kor\-te\-weg-de Vries (mKdV) equation is expressed in terms of the determinant
representation. Using this representation, the $n$-soliton solutions of the
mKdV equation are also expressed by determinants whose elements consist of the
eigenvalues $\lambda_{j}$ and the corresponding eigenfunctions of the
associated Lax equation. The nonsingular $n$-positon solutions of the focusing
mKdV equation are obtained in the special limit
$\lambda_{j}\rightarrow\lambda_{1}$, from the corresponding $n$-soliton
solutions and by using the associated higher-order Taylor expansion.
Furthermore, the decomposition method of the $n$-positon solution into $n$
single-soliton solutions, the trajectories, and the corresponding "phase
shifts" of the multi-positons are also investigated.