2017/05/19 by Qiuxia Xing, Xing, Qiuxia, Zhiwei Wu +5
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.48550/arxiv.1705.06836
17 pages, 7 figures. This is the accepted version by Nonlinear Dynamics
arxiv created 2017/05/19 · arxiv updated 2017/05/22
The n-fold Darboux transformation Tn 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 λj 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 λj→λ1, 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.