Generating mechanism and dynamic of the smooth positons for the derivative nonlinear Schrödinger equation

Abstract

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. Additional, 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.

arXiv comment11 pages,6 figures

References in corpus (5)

• A generating mechanism for higher order rogue waves
• The Darboux transformation of the derivative nonlinear Schrödinger equation
• Bilinearization of a Generalized Derivative Nonlinear Schrödinger equation
• Generation of higher-order rogue waves from multi-breathers by double degeneracy in an optical fibre
• Darboux transformation for two component derivative nonlinear Schrödinger equation

Cited by in corpus (1)

• Degenerate soliton solutions and their interactions in coupled Hirota equation with trivial and nontrivial background