Breather and double-pole solutions of the derivative nonlinear Schrödinger equation from optical fibers

In fluid dynamics, plasma physics and nonlinear optics, Korteweg-de Vries (KdV)-type equations are used to describe certain phenomena. In this paper, a coupled KdV-modified KdV system is investigated. Based on the Bell polynomials and symbolic computation, the bilinear form of such system is derived, and its analytic N-soliton solutions are constructed through the Hirota method. Two types of multi-soliton interactions are found, one with the reverse of solitonic shapes, and the other, without. Both the two types can be considered elastic. For a pair of solutions to such system, u and v, with the number of solitons N even, the soliton shapes of u stay unvaried while those of v reverse after the interaction; with N odd, the soliton shapes of both u and v keep unchanged after the interaction.

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“…More on the solitonic interactions can be seen in Refs. [34][35][36][37][38][39][40]. Taking N = 2, .…”

Section: Multi-soliton Interactionmentioning

confidence: 99%

Bell Polynomial Approach and N -Soliton Solutions for a Coupled KdV-mKdV System

Qin

Gao

et al. 2012

Commun. Theor. Phys.

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“…Recently, there is a growing interest in the degenerate cases of N-soliton solutions and their described soliton interactions (e.g. see [5][6][7][8][9][10][11][12][13] and references therein). Taking the focusing NLSE as an example, its bright N-soliton solutions admit two important degenerate cases.…”

Section: Introductionmentioning

confidence: 99%

“…In the context of optical fibers, the MPSs can describe the interactions of multiple chirped pulses of equal amplitudes, where the interaction force between two pulses decreases exponentially with their initial distance [15,17]. Besides, the MPSs, mostly in cases of double-pole solution, have also been revealed in many other integrable NLEEs [5,6,13,[18][19][20][21][22][23][24][25][26][27][28][29], and the nonintegrable subcritical and supercritical NLSEs [30].…”

Section: Introductionmentioning

confidence: 99%

Multi-pole solutions and their asymptotic analysis of the focusing Ablowitz–Ladik equation

Yue

2020

Phys. Scr.

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For the focusing Ablowitz–Ladik equation, the double- and triple-pole solutions are derived from its multi-soliton solutions via some limit technique. Also, the asymptotic analysis is performed for such two multi-pole solutions (MPSs) by considering the balance between exponential and algebraic terms. Like the continuous nonlinear Schrödinger equation, the discrete MPSs describe the elastic interactions of multiple solitons with the same amplitudes. But in contrast to the common multi-soliton solutions, most asymptotic solitons in the MPSs are localized in the curves of the nt plane, and thus they have the time-dependent velocities. In addition, the solitons’ relative distances grow logarithmically with , while the separation acceleration magnitudes decrease exponentially with their distance.

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