Smooth positon solutions of the focusing modified Korteweg–de Vries equation

Smooth positon solutions of the focusing modified Korteweg–de Vries equation The n-fold Darboux transformation $$T_{n}$$ T n of the focusing real modified Korteweg–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 $$\lambda _{j}$$ λ 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 $$\lambda _{j}\rightarrow \lambda _{1}$$ λ j → λ 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. Nonlinear Dynamics Springer Journals

Smooth positon solutions of the focusing modified Korteweg–de Vries equation

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Springer Netherlands
Copyright © 2017 by Springer Science+Business Media Dordrecht
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
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