On a Riemann–Hilbert problem for the NLS-MB equations
Abstract
In this paper, we study a coupled system of the nonlinear Schrödinger (NLS) equation and the Maxwell–Bloch (MB) equation with nonzero boundary conditions by Riemann–Hilbert (RH) method. We obtain the formulae of the simple-pole and the multi-pole solutions via a matrix Riemann–Hilbert problem (RHP). The explicit form of the soliton solutions for the NLS-MB equations is obtained. The soliton interaction is also given. Furthermore, we show that the multi-pole solutions can be viewed as some proper limits of the soliton solutions with simple poles, and the multi-pole solutions constitute a novel analytical viewpoint in nonlinear complex phenomena. The advantage of this way is that it avoids solving the complex symmetric relations and repeatedly solving residue conditions.
References
- 1. , Optical Solitons in Fibers (Springer, Berlin, Heidelberg, 1989), pp. 1–74. Crossref, Google Scholar
- 2. , Appl. Phys. Lett. 23(3) (1973) 142. Crossref, ISI, ADS, Google Scholar
- 3. , Phys. Rev. Lett. 18(21) (1967) 908. Crossref, ISI, ADS, Google Scholar
- 4. , Zh. Eksp. Teor. Fiz 85 (1983) 1177. ADS, Google Scholar
- 5. , Sov. Phys. JETP 58 (1983) 685. ADS, Google Scholar
- 6. , J. Phys. A: Math. Gen. 28(13) (1995) 3817. Crossref, ADS, Google Scholar
- 7. , Chaos Solitons Fractals 12(6) (2001) 1137. Crossref, ISI, ADS, Google Scholar
- 8. , Commun. Theoret. Phys. 38(4) (2002) 493. Crossref, ISI, ADS, Google Scholar
- 9. , Phys. Rev. E 86(6–2) (2012) 066603. Crossref, ISI, ADS, Google Scholar
- 10. , J. Phys. Soc. Japan 81(3) (2012) 033002. Crossref, Google Scholar
- 11. , Comput. Math. Math. Phys. 52(4) (2012) 565. Crossref, ISI, Google Scholar
- 12. , Z. Naturforsch. A 66(12) (2011) 712. Crossref, ISI, ADS, Google Scholar
- 13. Acta Math. Sci. 34(4) (2014) 973. Crossref, ISI, Google Scholar
- 14. , Appl. Math. Lett. 116 (2021) 107009. Crossref, ISI, Google Scholar
- 15. Optik 127(10) (2016) 4222. Crossref, ISI, ADS, Google Scholar
- 16. , East Asian J. Appl. Math. 10(3) (2020) 549. Crossref, ISI, Google Scholar
- 17. , AIMS Math. 5(3) (2020) 2461. Crossref, ISI, Google Scholar
- 18. , Mod. Phys. Lett. B 33(23) (2019) 1950277. Link, ISI, ADS, Google Scholar
- 19. , Eur. Phys. J. Plus 135(3) (2020) 1. Crossref, ISI, Google Scholar
- 20. , Eur. Phys. J. Plus 130(12) (2015) 1. Crossref, ISI, Google Scholar
- 21. , Int. J. Comput. Math. 98(7) (2021) 1457. Crossref, ISI, Google Scholar
- 22. , Int. J. Mod. Phys. B 25(22) (2011) 2965. Link, ISI, ADS, Google Scholar
- 23. , Phys. Rev. Lett. 66(20) (1991) 2625. Crossref, ISI, ADS, Google Scholar
- 24. , Phys. Rev. A 44(9) (1991) 5973. Crossref, ISI, ADS, Google Scholar
- 25. , Chaos Solitons Fractals 11(8) (2000) 1261. Crossref, ISI, ADS, Google Scholar
- 26. , Phys. Rev. Lett. 19 (1967) 1095. Crossref, ISI, ADS, Google Scholar
- 27. , Soliton, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, Cambridge, 1991). Crossref, Google Scholar
- 28. , Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, Philadelphia, 2010). Crossref, Google Scholar
- 29. , Ann. Math. 137 (1993) 295. Crossref, ISI, Google Scholar
- 30. , J. Differ. Equ. 269(11) (2020) 10322. Crossref, ISI, ADS, Google Scholar
- 31. , Int. J. Mod. Phys. B 35(4) (2021) 2150051. Link, ISI, ADS, Google Scholar
- 32. , J. Math. Anal. Appl. 498(2) (2021) 124980. Crossref, ISI, Google Scholar
- 33. , J. Math. Phys. 59(7) (2018) 073508. Crossref, ISI, Google Scholar
- 34. , Proc. Amer. Math. Soc. 149(1) (2021) 251. Crossref, ISI, Google Scholar
- 35. , J. Geom. Phys. 153 (2020) 103669. Crossref, ISI, Google Scholar
- 36. , Phys. D: Nonlinear Phenomena 417 (2021) 132811. Crossref, ISI, Google Scholar
- 37. , IMA J. Appl. Math. 82(1) (2017) 131. Crossref, ISI, Google Scholar
- 38. , J. Math. Phys. 55(3) (2014) 031506. Crossref, ISI, Google Scholar
- 39. , J. Math. Phys. 55(10) (2014) 101505. Crossref, ISI, ADS, Google Scholar
- 40. , J. Phys. Soc. Jpn. 63 (1994) 885. Crossref, ADS, Google Scholar
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