Numerical computation for rogue waves in the coupled nonlinear Schrödinger equations with the coherent coupling effect

References

• N. Akhmediev, A. Ankiewicz, and J.M. Soto-Crespo, Rogue waves and rational solutions of the nonlinear Schrödinger equation, Phys. Rev. E. 80 (2009), p. 026601.
   Web of Science ®Google Scholar
• X. Antoine, W. Bao, and C. Besse, Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations, Comput. Phys. Commun. 184 (2013), pp. 2621–2633.
   Web of Science ®Google Scholar
• H. Bailung, S.K. Sharma, and Y. Nakamura, Observation of Peregrine solitons in a multicomponent plasma with negative ions, Phys. Rev. Lett. 107 (2011), pp. 255005.
   PubMed Web of Science ®Google Scholar
• W. Bao and Y. Cai, Mathematical theory and numerical methods for Bose-Einstein condensation, Kinet. Relat. Models. 6 (2013), pp. 1–135.
   Web of Science ®Google Scholar
• W. Bao and Y. Cai, Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrödinger equation with wave operator, SIAM J. Numer. Anal. 52 (2014), pp. 1103–1127.
   Web of Science ®Google Scholar
• W. Bao, Q. Tang, and Z. Xu, Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation, J. Comput. Phys. 235 (2013), pp. 423–445.
   Web of Science ®Google Scholar
• F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, Vector rogue waves and baseband modulation instability in the defocusing regime, Phys. Rev. Lett. 113 (2014), pp. 034101.
   PubMed Web of Science ®Google Scholar
• F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves, Phys. Rev. Lett. 109 (2012), p. 044102.
   PubMed Web of Science ®Google Scholar
• H. Berland, A.L. Islas, and C.M. Schober, Conservation of phase space properties using exponential integrators on the cubic Schrödinger equation, J. Comput. Phys. 225 (2007), pp. 284–299.
   Web of Science ®Google Scholar
• C. Besse, G. Dujardin, and I. Lacroix-Violet, High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose–Einstein condensates, SIAM J. Numer. Anal. 55 (2017), pp. 1387–1411.
   Web of Science ®Google Scholar
• A. Calini, C.M. Schober, and M. Strawnb, Linear instability of the Peregrine breather: Numerical and analytical investigations, Appl. Numer. Math. 141 (2019), pp. 36–43.
   Web of Science ®Google Scholar
• A. Chabchoub, N. Hoffmann, and N. Akhmediev, Rogue wave observation in a water wave tank, Phys. Rev. Lett. 106 (2011), pp. 204502.
   PubMed Web of Science ®Google Scholar
• S. Chen, F. Baronio, J.M. Soto-Crespo, P. Grelu, and D. Mihalache, Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems, J. Phys. A 50 (2017), pp. 463001.
   Google Scholar
• J.M. Dudley, F. Dias, M. Erkintalo, and G. Genty, Instabilities, breathers and rogue waves in optics, Nat. Photon. 8 (2014), pp. 755–764.
   Web of Science ®Google Scholar
• J.M. Dudley, G. Genty, A. Mussot, A. Chabchoub, and F. Dias, Rogue waves and analogies in optics and oceanography, Nat. Rev. Phys. 1 (2019), pp. 675–689.
   Google Scholar
• B. Frisquet, B. Kibler, P. Morin, F. Baronio, M. Conforti, G. Millot, and S. Wabnitz, Optical dark rogue wave, Sci. Rep. 6 (2016), pp. 20785.
   PubMed Web of Science ®Google Scholar
• B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J.M. Dudely, The Peregrine soliton in nonlinear fibre optics, Nat. Phys. 6 (2010), pp. 790–795.
   Web of Science ®Google Scholar
• Y.S. Kivshar and G.P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic Press, San Diego, 2003.
   Google Scholar
• C. Klein and M. Haragus, Numerical study of the stability of the Peregrine solution, Ann. Math. Sci. Appl. 2 (2017), pp. 217–239.
   Web of Science ®Google Scholar
• C. Munoz, Instability in nonlinear Schrödinger breathers, Proyecciones. 36 (2017), pp. 653–683.
   Google Scholar
• Q.H. Park and H.J. Shin, Painlevé analysis of the coupled nonlinear Schrödinger equation for polarized optical waves in an isotropic medium, Phys. Rev. E. 59 (1999), pp. 2373–2379.
   Web of Science ®Google Scholar
• D.H. Peregrine, Water waves, nonlinear Schrödinger equations and their solutions, J. Austral. Math. Soc. B. 25 (1983), pp. 16–43.
   Web of Science ®Google Scholar
• D.R. Solli, C. Ropers, P. Koonath, and B. Jalali, Optical rogue waves, Nature 450 (2007), pp. 1054–1057.
   PubMed Web of Science ®Google Scholar
• G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal. 5 (1968), pp. 506–517.
   Web of Science ®Google Scholar
• W.R. Sun and L. Liu, Asymmetrical, rotational and ultra-high amplitude fundamental polarized optical rogue waves associated with the coherent coupling, Phys. Lett. A. 391 (2021), pp. 127132.
   Web of Science ®Google Scholar
• W.R. Sun, B. Tian, Y. Jiang, and H.L. Zhen, Optical rogue waves associated with the negative coherent coupling in an isotropic medium, Phys. Rev. E. 91 (2015), pp. 023205.
   Web of Science ®Google Scholar
• T.R. Taha and M.J. Ablowitz, Analytical and numerical aspects of certain nonlinear evolution equations. II. numerical, nonlinear Schrödinger equation, J. Comput. Phys. 55 (1984), pp. 203–230.
   Web of Science ®Google Scholar
• P. Wang, Z. Xu, and J. Yin, Simple high-order boundary conditions for computing rogue waves in the nonlinear Schrödinger equation, Comput. Phys. Commun. 251 (2020), pp. 107109.
   Web of Science ®Google Scholar
• H.Q. Zhang, J. Li, T. Xu, Y.X. Zhang, W. Hu, and B. Tian, Optical soliton solutions for two coupled nonlinear Schrödinger systems via Darboux transformation, Phys. Scr. 76 (2007), pp. 452–460.
   Web of Science ®Google Scholar