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Soliton and breather molecules in few-cycle-pulse optical model

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Abstract

The modified Korteweg–de Vries–sine-Gordon (mKdV–sG) equation is one of the models describing few-cycle-pulse optical solitons beyond the slowly varying envelope approximation. By introducing the velocity resonance mechanism to multiple soliton/breather solutions, it is found that the mKdV–sG model possesses abundant soliton molecule (SM), breather molecule (BM) and breather–soliton molecule (BSM) structures. Every SM includes only two solitons, a BM can be constructed by arbitrary number of breathers and a BSM can be formed from one or two solitons and arbitrary number of breathers. Though the interactions among the separated solitons and breathers are elastic, the size (the distances among solitons in a same molecule) will be changed after the interaction. Prospects of the studies overviewed in this work are given in the conclusions.

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References

  1. Leblond, H., Mihalache, D.: Models of few optical cycle solitons beyond the slowly varying envelope approximation. Phys. Rep. 523, 61–126 (2013)

    Article  MathSciNet  Google Scholar 

  2. Sazonov, S.V.: Extremely short and quasi-monochromatic electromagnetic solitons in a two-component medium. J. Exp. Theor. Phys. 92, 361–373 (2001)

    Article  Google Scholar 

  3. Leblond, H., Mihalache, D.: Few-optical-cycle solitons: modified Korteweg-de Vries sine-Gordon equation versus other non-slowly-varying-envelope-approximation models. Phys. Rev. A 79, 063835 (2009)

    Article  Google Scholar 

  4. Kosevich, A., Kovalev, A.: The supersonic motion of a crowdion: the one-dimensional model with nonlinear interaction between the nearest neighbours. Solid State Commun. 12, 763–765 (1973)

    Article  Google Scholar 

  5. Konno, K., Kameyama, W., Sanuki, H.: Effect of weak dislocation potential on nonlinear wave propagation in anharmonic crystal. J. Phys. Soc. Jpn. 37, 171–176 (1974)

    Article  Google Scholar 

  6. Bugay, A.N., Sazonov, S.V.: Faster-than-light propagation of electromagnetic solitons in nonequilibrium medium taking account of diffraction. J. Opt. B: Quantum Semiclassical Opt. 6, 328–335 (2004)

    Article  Google Scholar 

  7. Leblond, H., Mihalache, D.: Few-optical-cycle dissipative solitons. J. Phys. A Math. Theor. 43, 375205 (2010)

    Article  MathSciNet  Google Scholar 

  8. Leblond, H., Mihalache, D.: Few-optical-cycle solitons: modified Korteweg-de Vries sine-Gordon equation versus other non-slowly-varying-envelope-approximation models. Phys. Rev. A. 70, 063835 (2009)

    Article  Google Scholar 

  9. Chen, D.Y., Zhang, D.J., Deng, S.F.: The novel multi-soliton solutions of the mkdvsine-gordon equations. J. Phys. Soc. Jpn. 71, 658–659 (2002)

    Article  Google Scholar 

  10. Sun, Y.Y., Wu, H.: New breather solutions of the model describing few-optical-cycle solitons beyond the slowly varying envelope approximation. Phys. Scr. 88, 065001 (2013)

    Article  Google Scholar 

  11. Herink, G., Kurtz, F., Jalali, B., Solli, D.R., Ropers, C.: Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules. Science 356, 50–54 (2017)

    Article  Google Scholar 

  12. Krupa, K., Nithyanandan, K., Andral, U., Tchofo-Dinda, P., Grelu, P.: Real-time observation of internal motion within ultrafast dissipative optical soliton molecules. Phys. Rev. Lett. 118, 243901 (2017)

    Article  Google Scholar 

  13. Ryczkowski, P., Närhi, M., Billet, C., Merolla, J.M., Genty, G., Dudley, J.M.: Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser. Nat. Photon. 12, 221–227 (2018)

    Article  Google Scholar 

  14. Liu, X., Yao, X., Cui, Y.: Real-time observation of the buildup of soliton molecules. Phys. Rev. Lett. 121, 023905 (2018)

    Article  Google Scholar 

  15. Melchert, O., Willms, S., Bose, S., Yulin, A., Roth, B., Mitschke, F., Morgner, U., Babushkin, I., Demircan, A.: Soliton molecules with two frequencies. Phys. Rev. Lett. 123, 243905 (2019)

    Article  Google Scholar 

  16. Peng, J., Boscolo, S., Zhao, Z., Zeng, H.: Breathing dissipative solitons in mode-locked fiber lasers. Sci. Adv. 5, eaax1110 (2019)

    Article  Google Scholar 

  17. Xu, G., Gelash, A., Chabchoub, A., Zakharov, V., Kibler, B.: Breather wave molecules. Phys. Rev. Lett. 122, 084101 (2019)

    Article  Google Scholar 

  18. Lou, S.Y.: Soliton molecules and asymmetric solitons in three fifth order systems via velocity resonance. J. Phys. Commun. 4, 041002 (2020)

    Article  Google Scholar 

  19. Möller, M., Cheng, Y., Khan, S.D., Zhao, B., Zhao, K., Chini, M., Paulus, G.G., Chang, Z.: Dependence of high-order-harmonic-generation yield on driving-laser ellipticity. Phys. Rev. A 86, 011401 (2012)

    Article  Google Scholar 

  20. Dudley, J.M., Genty, G., Mussot, A., Chabchoub, A., Dias, F.: Rogue waves and analogies in optics and oceanography. Nat. Rev. Phys. 1, 675–689 (2019)

    Article  Google Scholar 

  21. Xu, D.H., Lou, S.Y.: Dark soliton molecules in nonlinear optics. Acta Phys. Sin. 69, 014208 (2020). (In Chinese)

    Google Scholar 

  22. Yan, Z., Lou, S.Y.: Soliton molecules in Sharma–Tasso–Olver–Burgers equation. Appl. Math. Lett. 104, 106271 (2020)

    Article  MathSciNet  Google Scholar 

  23. Zhang, Z., Yang, X., Li, B.: Soliton molecules and novel smooth positons for the complex modified KdV equation. Appl. Math. Lett. 103, 106168 (2020)

    Article  MathSciNet  Google Scholar 

  24. Cui, C.J., Tang, X.Y., Cui, Y.J.: New variable separation solutions and wave interactions for the \((3+1)\)-dimensional Boiti–Leon–Manna–Pempinelli equation. Appl. Math. Lett. 102, 106109 (2020)

    Article  MathSciNet  Google Scholar 

  25. Zhang, Z., Yang, X.Y., Li, B.: Novel soliton molecules and breather-positon on zero background for the complex modified KdV equation. Nonlinear Dyn. 100, 1551 (2020)

    Article  Google Scholar 

  26. Hirota, R.: Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27, 1192–1194 (1971)

    Article  Google Scholar 

  27. Zhang, D.J., Chen, D.Y.: The n-soliton solutions of the sine-gordon equation with self-consistent sources. Phys. A 321, 467–481 (2003)

    Article  MathSciNet  Google Scholar 

  28. Mirzazadeh, M., Ekici, M., Sonmezoglu, A., Eslami, M., Zhou, Q., Kara, A.H., Milovic, D., Majid, F.B., Biswas, A., Belić, M.: Optical solitons with complex Ginzburg–Landau equation. Nonlinear Dyn. 85, 1979–2016 (2016)

    Article  MathSciNet  Google Scholar 

  29. Brabec, T., Krausz, F.: Intense few-cycle laser fields: frontiers of nonlinear optics. Rev. Mod. Phys. 72, 545–591 (2000)

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank Prof. X. M. Liu for his helpful discussions. The work is supported by NNSFC (Nos. 11675084, 11835011, 11975131). The authors are sponsored by K. C. Wong Magna Fund in Ningbo University.

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Authors and Affiliations

  1. Laboratory of Clean Energy Storage and Conversion, School of Physical Science and Technology, Ningbo University, Ningbo, 315211, People’s Republic of China

    Man Jia & Sen Yue Lou

  2. Department of Physics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, People’s Republic of China

    Ji Lin

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  1. Man Jia
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  2. Ji Lin
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  3. Sen Yue Lou
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Correspondence to Man Jia.

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Jia, M., Lin, J. & Lou, S.Y. Soliton and breather molecules in few-cycle-pulse optical model. Nonlinear Dyn 100, 3745–3757 (2020). https://doi.org/10.1007/s11071-020-05695-3

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  • DOI: https://doi.org/10.1007/s11071-020-05695-3

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