Stability is an essential problem in theoretical and experimental studies of solitons in nonlinear media with fractional diffraction, which is represented by the Riesz derivative with Lévy index (LI) , taking values . Fractional solitons are unstable at or in uniform one-dimensional media with the cubic or quintic self-focusing, respectively. We demonstrate that, in these cases, the solitons may be effectively stabilized by pinning to a delta-functional trapping potential (attractive defect), which is a relevant setting in optical waveguides with the effective fractional diffraction. Using the respective fractional nonlinear Schrödinger equation with the delta-functional potential term, we find that, in the case of the cubic self-focusing, the fractional solitons are fully stabilized by the pinning to the defect for and partly stabilized for . In the case of the quintic self-focusing, the full and partial stabilization are found for and , respectively. In both cases, the instability boundary is exactly predicted by the Vakhitov–Kolokolov criterion. Unstable solitons spontaneously transform into oscillating breathers. A variational approximation (VA) is elaborated parallel to the numerical analysis, with a conclusion that the VA produces accurate results for lower LI values, i.e., stronger fractionality. In the cubic medium, collisions of traveling stable solitons with repulsive and attractive defects are addressed too, demonstrating outcomes in the form of rebound, splitting, and passage.
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Interactions of fractional solitons with local defects: Stabilization and scattering
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March 2025
Research Article|
March 19 2025
Interactions of fractional solitons with local defects: Stabilization and scattering
Special Collection:
Advances in Mathematics and Physics: from Complexity to Machine Learning
Thawatchai Mayteevarunyoo
;
Thawatchai Mayteevarunyoo
a)
(Data curation, Methodology, Writing – original draft, Writing – review & editing)
1
Department of Electrical and Computer Engineering, Faculty of Engineering, Naresuan University
, Phitsanulok 65000, Thailand
a)Author to whom correspondence should be addressed: [email protected]
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Boris A. Malomed
Boris A. Malomed
(Conceptualization, Writing – original draft, Writing – review & editing)
2
Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University
, P.O.B. 39040, Ramat Aviv, Tel Aviv, Israel
3
Instituto de Alta Investigación, Universidad de Tarapacá
, Casilla 7D, Arica, Chile
Search for other works by this author on:
Thawatchai Mayteevarunyoo
1,a)
Boris A. Malomed
2,3
1
Department of Electrical and Computer Engineering, Faculty of Engineering, Naresuan University
, Phitsanulok 65000, Thailand
2
Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University
, P.O.B. 39040, Ramat Aviv, Tel Aviv, Israel
3
Instituto de Alta Investigación, Universidad de Tarapacá
, Casilla 7D, Arica, Chile
a)Author to whom correspondence should be addressed: [email protected]
Chaos 35, 033138 (2025)
Article history
Received:
January 19 2025
Accepted:
February 26 2025
Citation
Thawatchai Mayteevarunyoo, Boris A. Malomed; Interactions of fractional solitons with local defects: Stabilization and scattering. Chaos 1 March 2025; 35 (3): 033138. https://doi.org/10.1063/5.0259305
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