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Observation of Kuznetsov-Ma soliton dynamics in optical fibre.

Kibler B, Fatome J, Finot C, Millot G, Genty G, Wetzel B, Akhmediev N, Dias F, Dudley JM - Sci Rep (2012)

Bottom Line: However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity.We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE.Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS - Universite´ de Bourgogne, Dijon, France.

ABSTRACT
The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

Show MeSH
Analytic solutions of the NLSE from Eq. (2) with different values of parameter a as indicated illustrating the three different classes of primary soliton on finite background solutions of the NLSE.
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f1: Analytic solutions of the NLSE from Eq. (2) with different values of parameter a as indicated illustrating the three different classes of primary soliton on finite background solutions of the NLSE.

Mentions: We plot the solution of Eq. (2) for different values of a in Fig. 1. For a < ½ as shown in Fig. 1(a) the solution describes the Akhmediev breather, and ω and b are real with physical significance as a modulation frequency and exponential growth and decay rate. We see clearly the growth and decay cycle of the initial weak periodic modulation. For a = ½ as in Fig. 1(b), the solution describes the Peregrine soliton corresponding to the low frequency limit of the Akhmediev breather which in this case is localized in both transverse and longitudinal dimensions. For a > ½ as in Fig. 1(c), the solution describes the KM soliton where the parameters ω and b become imaginary such that the hyperbolic trigonometric functions in Eq. (2) become ordinary circular functions and vice-versa. It is this that leads to the contrasting localization and periodicity characteristics and different physics of the Akhmediev and KM solutions.


Observation of Kuznetsov-Ma soliton dynamics in optical fibre.

Kibler B, Fatome J, Finot C, Millot G, Genty G, Wetzel B, Akhmediev N, Dias F, Dudley JM - Sci Rep (2012)

Analytic solutions of the NLSE from Eq. (2) with different values of parameter a as indicated illustrating the three different classes of primary soliton on finite background solutions of the NLSE.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3376454&req=5

f1: Analytic solutions of the NLSE from Eq. (2) with different values of parameter a as indicated illustrating the three different classes of primary soliton on finite background solutions of the NLSE.
Mentions: We plot the solution of Eq. (2) for different values of a in Fig. 1. For a < ½ as shown in Fig. 1(a) the solution describes the Akhmediev breather, and ω and b are real with physical significance as a modulation frequency and exponential growth and decay rate. We see clearly the growth and decay cycle of the initial weak periodic modulation. For a = ½ as in Fig. 1(b), the solution describes the Peregrine soliton corresponding to the low frequency limit of the Akhmediev breather which in this case is localized in both transverse and longitudinal dimensions. For a > ½ as in Fig. 1(c), the solution describes the KM soliton where the parameters ω and b become imaginary such that the hyperbolic trigonometric functions in Eq. (2) become ordinary circular functions and vice-versa. It is this that leads to the contrasting localization and periodicity characteristics and different physics of the Akhmediev and KM solutions.

Bottom Line: However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity.We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE.Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS - Universite´ de Bourgogne, Dijon, France.

ABSTRACT
The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

Show MeSH