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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.

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(a) Input field comparing ideal KM solution and modulation approximation. (b) Integrating the NLSE for the modulated input field shows complex evolution. (c) The evolution for the central region of the NLSE simulation results agrees very well with the evolution of the ideal KM soliton.
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f2: (a) Input field comparing ideal KM solution and modulation approximation. (b) Integrating the NLSE for the modulated input field shows complex evolution. (c) The evolution for the central region of the NLSE simulation results agrees very well with the evolution of the ideal KM soliton.

Mentions: This approach is shown in Fig. 2, where we use numerical integration of the NLSE to compare the evolution of an input field based on an exact KM soliton with that of a suitably designed strongly-modulated field that approximates the KM soliton over each modulation cycle (see Methods). We first compare the two initial profiles used in the simulations in Fig. 2(a). Specifically, we choose the initial conditions of a strongly-modulated continuous wave (dashed line) such that the central modulation cycle overlaps with the KM soliton pulse above the background as shown (solid line) at a point of minimal intensity in its evolution. The governing parameter of the KM soliton in this case is aKM = 1.


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)

(a) Input field comparing ideal KM solution and modulation approximation. (b) Integrating the NLSE for the modulated input field shows complex evolution. (c) The evolution for the central region of the NLSE simulation results agrees very well with the evolution of the ideal KM soliton.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: (a) Input field comparing ideal KM solution and modulation approximation. (b) Integrating the NLSE for the modulated input field shows complex evolution. (c) The evolution for the central region of the NLSE simulation results agrees very well with the evolution of the ideal KM soliton.
Mentions: This approach is shown in Fig. 2, where we use numerical integration of the NLSE to compare the evolution of an input field based on an exact KM soliton with that of a suitably designed strongly-modulated field that approximates the KM soliton over each modulation cycle (see Methods). We first compare the two initial profiles used in the simulations in Fig. 2(a). Specifically, we choose the initial conditions of a strongly-modulated continuous wave (dashed line) such that the central modulation cycle overlaps with the KM soliton pulse above the background as shown (solid line) at a point of minimal intensity in its evolution. The governing parameter of the KM soliton in this case is aKM = 1.

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