151
Views
8
CrossRef citations to date
0
Altmetric
Research Articles

Three-wave resonant interactions: dark–bright–bright mixed N- and high-order solitons, breathers, and their structures

, , , &
Pages 3368-3380 | Received 05 Feb 2021, Accepted 30 Aug 2021, Published online: 30 Sep 2021

References

  • Baronio F, Degasperis A, Conforti M, et al. Solutions of the vector nonlinear Schröinger equations: evidence for deterministic Rogue waves. Phys Rev Lett. 2012;109:044102.
  • Chow KW, Chan HN, Kedziora DJ, et al. Rogue wave modes for the long wave? Short wave resonance model. J Phys Soc Jpn. 2013;82:074001.
  • Zhao XH. Dark soliton solutions for a coupled nonlinear Schrdinger system. Appl Math Lett. 2021;121:107383.
  • Gao XY, Guo YJ, Shan WR. Water-wave symbolic computation for the Earth, Enceladus and Titan: the higher-order Boussinesq-Burgers system, auto- and non-auto-Backlund transformations. Appl Math Lett. 2020;104:106170.
  • Gao XY, Guo YJ, Shan WR. Shallow water in an open sea or a wide channel: Auto- and non-auto-Backlund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system. Chaos Solitons Fract. 2020;138:109950.
  • Chen SS, Tian B, Sun Y, et al. Generalized darboux transformations, rogue waves, and modulation instability for the coherently coupled nonlinear Schrodinger equations in nonlinear optics. Ann Phys. (Berlin). 2019;531:1900011.
  • Tian HY, Tian B, Yuan YQ, et al. Superregular solutions for a coupled nonlinear Schrodinger system in a two-mode nonlinear fiber. Phys Scr. 2021;96:045213.
  • Wang M, Tian B, Hu CC, et al. Generalized Darboux transformation, solitonic interactions and bound states for a coupled fourth-order nonlinear Schrodinger system in a birefringent optical fiber. Appl Math Lett. 2021;119:106936.
  • Yang DY, Tian B, Qu QX, et al. Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiber. Chaos Solitons Fract. 2021;150:110487.
  • Gao XT, Tian B, Shen Y, Feng CH. Comment on “Shallow water in an open sea or a wide channel: Auto- and non-auto-Bäcklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system”, Chaos Solitons Fract. 2021;151: 111222.
  • Hu CC, Tian B, Yin HM, Zhang CR, Zhang Z. Dark breather waves, dark lump waves and lump wave-soliton interactions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in a fluid, Comput. Math. Appl. 2019;78: 166–177.
  • Shen Y, Tian B. Bilinear auto-Bäcklund transformations and soliton solutions of a (3 + 1)-dimensional generalized nonlinear evolution equation for the shallow water waves, Appl. Math. Lett. 2021;122:107301.
  • Zakharov VE, Manakov SV. Resonance interaction of wave packets. Zh Eksp Teor Fiz Pisma Red. 1973;18:413.
  • Kaup DJ. The three-wave interaction – a nondispersive phenomenon. Stud Appl Math. 1976;55:9.
  • Kaup DJ, Reiman A, Bers A, et al. Space-time evolution of nonlinear three-wave interactions.I. Interaction in a homogeneous medium. Rev Mod Phys. 1979;51:275.
  • Craik A. Wave interactions and fluid flows. Cambridge: Cambridge University Press; 1988.
  • Lamb KG. Tidally generated near-resonant internal wave triads at a shelf break. Geophys Res Lett. 2007;34:L186071.
  • Baronio F, Conforti M, De Angelis C, et al. Velocity-locked solitary waves in quadratic media. Phys Rev Lett. 2010;104:113902.
  • Franklin RN. Microinstabilities in plasmas-non-linear effects. Rep Prog Phys. 1977;40:1369.
  • Dodin IY, Fisch NJ. Storing, retrieving, and processing optical information by Raman backscattering in plasmas. Phys Rev Lett. 2002;88:165001.
  • Burlak G, Koshevaya S, Hayakawa M, et al. Acousto-optic solitons in fibers. Opt Rev. 2000;7:323.
  • Degasperis A, Lombardo S. Rational solitons of wave resonant-interaction models. Phys Rev E. 2013;88:052914.
  • Wang X, Cao JL, Chen Y. Higher-order rogue wave solutions of the three-wave resonant interaction equation via the generalized Darboux transformation. Phys Scr. 2015;90:105201.
  • Zhang GQ, Yan ZY, Wen XY. Three-wave resonant interactions: multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics. Phys D. 2018;366:27.
  • Guo LJ, He JS, Mihalache D. Rational and semi-rational solutions to the asymmetric Nizhnik-Novikov-Veselov system. J Phys A. 2021;54:095703.
  • Rao JG, He JS, Mihalache D, et al. Dynamics of lump-soliton solutions to the PT-symmetric nonlocal Fokas system, Wave Motion. 2021;101:102685.
  • Rao JG, He JS, Mihalache D, et al. PT-symmetric nonlocal Davey-Stewartson I equation: general lump-soliton solutions on a background of periodic line waves. Appl Math Lett. 2021;104:106246.
  • Hou C, Bu LL, Baronio F, et al. Sine-Gordon breathers and formation of extreme waves in self-induced transparency media. Rom Rep Phys. 2020;72:405.
  • Cheng CD, Tian B, Zhang CR, et al. Bilinear form, soliton, breather, hybrid and periodic-wave solutions for a (3+1)-dimensional Korteweg-de Vries equation in a fluid. Nonlinear Dyn. 2021;105:2525.
  • Liu SH, Tian B, Qu QX, et al. Breather, lump, shock and travelling-wave solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid mechanics and plasma physics. Int J Comput Math. 2021;98:1130–1145.
  • Zhao X, Tian B, Tian HY, et al. Bilinear Backlund transformation, Lax pair and interactions of nonlinear waves for a generalized (2+1)-dimensional nonlinear wave equation in nonlinear optics/fluid mechanics/plasma physics. Nonlinear Dyn. 2021;103:1785–1794.
  • Wang M, Tian B, Sun Y, et al. Lump, mixed lump-stripe and rogue wave-stripe solutions of a (3+1)-dimensional nonlinear wave equation for a liquid with gas bubbles. Comput Math Appl. 2020;79:576–587.
  • Ma YX, Tian B, Qu QX, et al. Painleve analysis, Backlund transformations and traveling-wave solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in a fluid. Int J Mod Phys B. 2021;35:2150108.
  • Zhang CR, Tian B, Qu QX, Liu L, Tian HY. Vector bright solitons and their interactions of the couple Fokas-Lenells system in a birefringent optical fiber, Z. Angew. Math. Phys. 2020;71:18.
  • Wei CC, Tian B, Qu QX, Chen SS, Yang DY. Lax pair, Darboux transformation and rogue-periodic waves of a nonlinear Schrodinger-Hirota equation with the spatio-temporal dispersion and Kerr law nonlinearity in nonlinear optics, Mod. Phys. Lett. B 2021;33: 2150451.
  • Ma YX, Tian B, Qu QX, Wei CC, Zhao X. Backlund transformations, kink soliton, breather- and travelling-wave solutions for a (3+1)-dimensional B-type Kadomtsev-Petviashvili equation in fluid dynamics, Chin. J. Phys. 2021;73: 600–612.
  • Zhang GQ, Yan ZY. Three-component nonlinear Schördinger equations: modulational instability, Nth-order vector rational and semi-rational rogue waves, and dynamics. Commun Nonlinear Sci Numer Simul. 2018;62:117.
  • Yan ZY. Vector financial rogue waves. Phys Lett A. 2011;375:4274.
  • Guo BL, Ling LM, Liu QP. Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions. Phys Rev E. 2012;85:026607.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.