386
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

The dynamical behavior of mixed-type soliton solutions described by (2+1)-dimensional Bogoyavlensky–Konopelchenko equation with variable coefficients

ORCID Icon & ORCID Icon
Pages 1457-1464 | Received 17 Dec 2017, Accepted 20 Feb 2018, Published online: 27 Feb 2018

References

  • Yang XJ , Tenreiro Machado JA , Baleanu D , et al . On exact traveling-wave solutions for local fractional Korteweg-de Vries equation. Chaos Interdisc J Nonlinear Sci. 2016;26(8):084312.
  • Osman MS . On complex wave solutions governed by the 2D Ginzburg--Landau equation with variable coefficients. Opt Int J Light Electron Opt. 2018;156:169–174.
  • Inc M , Yusuf A , Aliyu AI , et al . Optical soliton solutions for the higher-order dispersive cubic-quintic nonlinear Schrödinger equation. Superlattices Microstruct. 2017;112:164–179.
  • Osman MS , Wazwaz AM . An efficient algorithm to construct multi-soliton rational solutions of the (2+1)-dimensional KdV equation with variable coefficients. Appl Math Comput. 2018;321:282–289.
  • Huang LL , Chen Y . Lump solutions and interaction phenomenon for (2+1)-dimensional Sawada--Kotera equation. Commun Theor Phys. 2017;67:473–478.
  • Bell ET . Exponential polynomials. Ann Math. 1934;35:258–277.
  • Lü X , Li J . Integrability with symbolic computation on the Bogoyavlensky--Konoplechenko model: Bell-polynomial manipulation, bilinear representation, and Wronskian solution. Nonlinear Dyn. 2014;77(1–2):135–143.
  • Lambert F , Springael J . Construction of Bäcklund transformations with binary Bell polynomials. J Phys Soc Jpn. 1997;66:2211.
  • Osman MS . On multi-soliton solutions for the (2+1)-dimensional breaking soliton equation with variable coefficients in a graded-index waveguide. Comput Math Appl. 2018;75(1):1–6.
  • Osman MS . Nonlinear interaction of solitary waves described by multi-rational wave solutions of the (2+1)-dimensional Kadomtsev--Petviashvili equation with variable coefficients. Nonlinear Dyn. 2017;87(2):1209–1216.
  • Osman MS . Multi-soliton rational solutions for some nonlinear evolution equations. Open Phys. 2016;14(1):26–36.
  • Osman MS . Multi-soliton rational solutions for quantum Zakharov--Kuznetsov equation in quantum magnetoplasmas. Wave Random Complex. 2016;26(4):434–443.
  • Osman MS . Analytical study of rational and double-soliton rational solutions governed by the KdV-Sawada--Kotera--Ramani equation with variable coefficients. Nonlinear Dyn. 2017;89(3):2283–2289.
  • Gardner CS , Greene JM , Kruskal MD , et al . Method for solving the Korteweg-de Vries equation. Phys Rev E. 1976;19(19):1095.
  • Wazwaz AM . The Hirota’s bilinear method and the tanh-coth method for multiple-soliton solutions of the Sawada--Kotera--Kadomtsev--Petviashvili equation. Appl Math Comput. 2008;200(1):160–166.
  • Hirota R . Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons. Phys Rev Lett. 1971;27(18):1192–1194.
  • Hietarinta J . A search for bilinear equations passing Hirota’s three-soliton condition I KdV-type bilinear equations. J Math Phys. 1987;28(8):1732–1742.
  • Li BQ , Ma YL , Mo LP , et al . The N-loop soliton solutions for (2+1)-dimensional Vakhnenko equation. Comput Math Appl. 2017;74(3):504–512.
  • Li BQ , Ma YL , Yang TM . The oscillating collisions between the three solitons for a dual-mode fiber coupler system. Superlattice Microstruct. 2017;110:126–132.
  • Ma YL , Li BQ . The wrinkle-like N-solitons for the thermophoretic motion equation through graphene sheets. Phys A. 2018;494:169–174.
  • Ablowitz MJ , Clarkson PA . Soliton, nonlinear evolution equations and inverse scattering. Vol. 149. Cambridge: Cambridge University Press; 1991.
  • Gu C . Soliton theory and its application, 1995. ( NASA STI/Recon Technical Report A 1).
  • Wang M , Li X , Zhang J . The (G'/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys Lett A. 2008;372(4):417–423.
  • Li B , Ma Y . The non-traveling wave solutions and novel fractal soliton for the (2+1)-dimensional Broer--Kaup equations with variable coefficients. Commun Nonlinear Sci Numer Simul. 2011;16(1):144–149.
  • Li BQ , Ma YL . New application of the (G'/G)-expansion method to excite soliton structures for nonlinear equation. Z Naturforsch A. 2010;65(6–7):518–524.
  • Hu HC . New positon, negaton and complexiton solutions for the Bogoyavlensky--Konoplechenko equation. Phys Lett A. 2009;373(20):1750–1753.
  • Xin XP , Liu XQ , Zhang LL . Explicit solutions of the Bogoyavlensky--Konoplechenko equation. Appl Math Comput. 2010;215(10):3669–3673.
  • Calogero F . A method to generate solvable nonlinear evolution equationsm Lett. Nuovo Cimento. 1975;14(12):443–447.
  • Bogoyavlenskii OI . Overturning solitons in new two-dimensional integrable equations. Izv Akad Nauk SSSR Ser Mat. 1989;53(2):243–257.
  • Ma WX , Gao L . Coupling integrable couplings. Mod Phys Lett B. 2009;23(15):1847–1860.
  • Konopelchenko BG . Solitons in multidimensions. Singapore: World Scientific; 1993.
  • Toda K , Yu SJ . A study of the construction of equations in (2+1)-dimensions. Inverse Probl. 2001;17(4):1053–1060.
  • Osman MS , Abdel-Gawad HI . Multi-wave solutions of the (2+1)-dimensional Nizhnik--Novikov--Veselov equations with variable coefficients. Eur Phys J Plus. 2015;130(10):1–11.
  • Abdel-Gawad HI , Osman MS . Exact solutions of the Korteweg-de Vries equation with space and time dependent coefficients by the extended unified method. Indian J Pure Appl Math. 2014;45(1):1–11.
  • Osman MS . Multiwave solutions of time-fractional (2+1)-dimensional Nizhnik--Novikov--Veselov equations. Pramana. 2017;88(4):67.
  • Abdel-Gawad HI , Tantawy M , Osman MS . Dynamic of DNA’s possible impact on its damage. Math Methods Appl Sci. 2016;39(2):168–176.
  • Osman MS , Machado JAT , Baleanu D . On nonautonomous complex wave solutions described by the coupled Schrödinger-Boussinesq equation with variable-coefficients. Opt Quant Electron. 2018;50(2):73.

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.