Soliton collisions for the Kundu–Eckhaus equation with variable coefficients in an optical fiber
| Autor: | Ze-Hui Yan, Xi-Yang Xie |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Asymptotic analysis
Optical fiber Applied Mathematics Bilinear form 01 natural sciences law.invention Nonlinear system Nonlinear Sciences::Exactly Solvable and Integrable Systems Amplitude law Quantum mechanics 0103 physical sciences Femtosecond Soliton 010306 general physics Nonlinear Sciences::Pattern Formation and Solitons 010301 acoustics Variable (mathematics) Mathematics |
| Zdroj: | Applied Mathematics Letters. 80:48-53 |
| ISSN: | 0893-9659 |
| Popis: | Under investigation in this paper is a Kundu–Eckhaus equation with variable coefficients, which models the propagation of the ultra-short femtosecond pulses in an optical fiber. Bright one- and two-soliton solutions for this equation are constructed, based on the bilinear forms obtained. Then, by the aid of the solutions, propagation of the one solitons and collisions between the two solitons are illustrated in figures, and with the help of the asymptotic analysis on the two-soliton solutions, the collisions are proved to be elastic. Influences of r ( x ) and m ( x ) on the solitons are also be analyzed, where r ( x ) and m ( x ) are respectively the group velocity dispersion and nonlinearity parameter: When they are both chosen as the constants, it can be found that the one solitons propagate with unvarying velocities and amplitudes, and shapes of the two solitons are maintained before and after the collisions; r ( x ) and m ( x ) are found to affect the velocities and amplitudes of the solitons, respectively. |
| Databáze: | OpenAIRE |
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