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Novel asymmetric representation method for solving the higher-order Ginzburg-Landau equation.

Wong P, Pang L, Wu Y, Lei M, Liu W - Sci Rep (2016)

Bottom Line: The analytic soliton solution is obtained for the first time, and is proved to be stable against amplitude perturbations.The analytic results here may extend the integrable methods, and could be used to study soliton dynamics for some equations in other disciplines.It may also provide the other way to obtain two-soliton solutions for higher-order GL equations.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China.

ABSTRACT
In ultrafast optics, optical pulses are generated to be of shorter pulse duration, which has enormous significance to industrial applications and scientific research. The ultrashort pulse evolution in fiber lasers can be described by the higher-order Ginzburg-Landau (GL) equation. However, analytic soliton solutions for this equation have not been obtained by use of existing methods. In this paper, a novel method is proposed to deal with this equation. The analytic soliton solution is obtained for the first time, and is proved to be stable against amplitude perturbations. Through the split-step Fourier method, the bright soliton solution is studied numerically. The analytic results here may extend the integrable methods, and could be used to study soliton dynamics for some equations in other disciplines. It may also provide the other way to obtain two-soliton solutions for higher-order GL equations.

No MeSH data available.


Soliton profiles of different cases.(a) w = 1, ε = 1, C1 = 2, C2 = 0, B1/B2 = −2; (b) w = 1, ε = 1, C1 = 2, C2 = 2, B1/B2 = −2; (c) w = 1, ε = 1, C1 = 2, C2 = 0, B1/B2 = −3.5.
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f1: Soliton profiles of different cases.(a) w = 1, ε = 1, C1 = 2, C2 = 0, B1/B2 = −2; (b) w = 1, ε = 1, C1 = 2, C2 = 2, B1/B2 = −2; (c) w = 1, ε = 1, C1 = 2, C2 = 0, B1/B2 = −3.5.

Mentions: If , the soliton is in the sech form. Otherwise, the soliton is asymmetric. Even more, if the equation contains another variable, it will be more free to obtain one-soliton solution. The structure of the equation has soliton solutions without the bilinear symmetric representation, which extends the integrable structures. For the special values of parameters, we can show the soliton profiles in Fig. 1.


Novel asymmetric representation method for solving the higher-order Ginzburg-Landau equation.

Wong P, Pang L, Wu Y, Lei M, Liu W - Sci Rep (2016)

Soliton profiles of different cases.(a) w = 1, ε = 1, C1 = 2, C2 = 0, B1/B2 = −2; (b) w = 1, ε = 1, C1 = 2, C2 = 2, B1/B2 = −2; (c) w = 1, ε = 1, C1 = 2, C2 = 0, B1/B2 = −3.5.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4834569&req=5

f1: Soliton profiles of different cases.(a) w = 1, ε = 1, C1 = 2, C2 = 0, B1/B2 = −2; (b) w = 1, ε = 1, C1 = 2, C2 = 2, B1/B2 = −2; (c) w = 1, ε = 1, C1 = 2, C2 = 0, B1/B2 = −3.5.
Mentions: If , the soliton is in the sech form. Otherwise, the soliton is asymmetric. Even more, if the equation contains another variable, it will be more free to obtain one-soliton solution. The structure of the equation has soliton solutions without the bilinear symmetric representation, which extends the integrable structures. For the special values of parameters, we can show the soliton profiles in Fig. 1.

Bottom Line: The analytic soliton solution is obtained for the first time, and is proved to be stable against amplitude perturbations.The analytic results here may extend the integrable methods, and could be used to study soliton dynamics for some equations in other disciplines.It may also provide the other way to obtain two-soliton solutions for higher-order GL equations.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China.

ABSTRACT
In ultrafast optics, optical pulses are generated to be of shorter pulse duration, which has enormous significance to industrial applications and scientific research. The ultrashort pulse evolution in fiber lasers can be described by the higher-order Ginzburg-Landau (GL) equation. However, analytic soliton solutions for this equation have not been obtained by use of existing methods. In this paper, a novel method is proposed to deal with this equation. The analytic soliton solution is obtained for the first time, and is proved to be stable against amplitude perturbations. Through the split-step Fourier method, the bright soliton solution is studied numerically. The analytic results here may extend the integrable methods, and could be used to study soliton dynamics for some equations in other disciplines. It may also provide the other way to obtain two-soliton solutions for higher-order GL equations.

No MeSH data available.