Generating mechanism and dynamic of the smooth positons for the derivative nonlinear Schrödinger equation. (English) Zbl 1430.35212
Summary: Based on the degenerate Darboux transformation, the \(n\)-order smooth positon solutions for the derivative nonlinear Schrödinger equation are generated by means of the general determinant expression of the \(N\)-soliton solution, and interesting dynamic behaviors of the smooth positons are shown by the corresponding three-dimensional plots in this paper. Furthermore, the decomposition process, bent trajectory and the change of the phase shift for the positon solutions are discussed in detail. Additionally, three kinds of mixed solutions, namely (1) the hybrid of one-positon and two-positon solutions, (2) the hybrid of two-positon and two-positon solutions, and (3) the hybrid of one-soliton and three-positon solutions, are presented and their rather complicated dynamics are revealed.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 35C08 | Soliton solutions |
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