Exact solutions and bifurcation for the resonant nonlinear Schrödinger equation with competing weakly nonlocal nonlinearity and fractional temporal evolution

References

• Hossen MB, Roshid H-O, Ali MZ. Characteristics of the solitary waves and rogue waves with interaction phenomena in a (2+1)-dimensional breaking soliton equation. Phys Lett A. 2018;382(19):1268–1274.
   Web of Science ®Google Scholar
• Girgis L, Milovic D, Konar S, et al. Optical gaussons in birefringent fibers and dwdm systems with inter-modal dispersion. Rom Rep Phys. 2012;64:663.
   Web of Science ®Google Scholar
• Zhou Q, Liu L, Liu Y, et al. Exact optical solitons in metamaterials with cubic–quintic nonlinearity and third-order dispersion. Nonlinear Dyn. 2015;80(3):1365–1371.
   Web of Science ®Google Scholar
• Abbou F, Hean Teik C, Majumder S. Limitations of soliton transmission in a cascaded optical amplifier system. J Opt Commun. 2000;21:165–170.
   Google Scholar
• Roshid H-O, Kabir MR, Bhowmik RC, et al. Investigation of solitary wave solutions for Vakhnenko–Parkes equation via exp-function and exp ( −φ (ξ))-expansion method. Springer Plus. 2014;3(1):692.
   PubMedGoogle Scholar
• Khatun MS, Hoque MF, Rahman MA. Multi solutions, completely elastic collisions and non-elastic fusion phenomena of two PDES. Pramana. 2017;88(6):86.
   Web of Science ®Google Scholar
• Rahman MA, et al. The exp ( −φ (η))-expansion method with application in the (1+1)-dimensional classical Boussinesq equations. Results Phys. 2014;4:150–155.
   Web of Science ®Google Scholar
• Hossen MB, Roshid H-O, Ali MZ. Modified double sub-equation method for finding complexiton solutions to the (1+1) dimensional nonlinear evolution equations. Int J Appl Comput Math. 2017;3(1):679–697.
   Google Scholar
• Harun-Or-Roshid. Kink type traveling wave solutions of right-handed non-commutative burgers equations via extended (g'g)-expansion method. Phys Sci Int J. 2019;21(4):1–6.
   Google Scholar
• Roshid H-O. Multi-soliton of the (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff equation and kdv equation. Comput Methods Differ Equ. 2019;7(1):86–95.
   Web of Science ®Google Scholar
• Ma W-X, et al. Dynamics of mixed lump-solitary waves of an extended (2+1)-dimensional shallow water wave model. Phys Lett A. 2018;382(45):3262–3268.
   Web of Science ®Google Scholar
• Roshid H-O. Lump solutions to a (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (ytsf) like equation. Int J Appl Comp Math. 2017;3:1455–1461.
   Google Scholar
• Mihalache D, Mazilu D, Lederer F, et al. Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media. Phys Rev E. 2006;73(2):025601.
   Google Scholar
• Mihalache D. Linear and nonlinear light bullets: recent theoretical and experimental studies. Rom J Phys. 2012;57(1–2):352–371.
   Web of Science ®Google Scholar
• Chen L, Wang Q, Shen M, et al. Nonlocal dark solitons under competing cubic–quintic nonlinearities. Opt Lett. 2013;38(1):13–15.
   PubMed Web of Science ®Google Scholar
• Zhou Q, Zhu Q, Liu Y, et al. Bright-dark combo optical solitons with non-local nonlinearity in parabolic law medium. Optoelectron Adv Mater Rapid Commun. 2014;8(9–10):837–839.
   Web of Science ®Google Scholar
• Zhou Q, Zhu Q. Theoretical study of dark solitons in media with competing nonlocal nonlinearities and local quintic nonlinearity. J Mod Opt. 2014;61(18):1465–1469.
   Web of Science ®Google Scholar
• Triki H, Hayat T, Aldossary OM, et al. Bright and dark solitons for the resonant nonlinear Schrödinger's equation with time-dependent coefficients. Opt Laser Technol. 2012;44(7):2223–2231.
   Web of Science ®Google Scholar
• Rogers C, Yip L, Chow K. A resonant Davey–Stewartson capillarity model system: solitonic generation. Int J Nonlinear Sci Numer Simul. 2009;10(3):397–405.
   Web of Science ®Google Scholar
• Pashaev OK, Lee JH. Resonance solitons as black holes in Madelung fluid. Modern Phys Lett A. 2002;17(24):1601–1619.
   Web of Science ®Google Scholar
• Das A. Optical solitons for the resonant nonlinear Schrödinger equation with competing weakly nonlocal nonlinearity and fractional temporal evolution. Nonlinear Dyn. 2017;90(3):2231–2237.
   Web of Science ®Google Scholar
• Królikowski W, Bang O. Solitons in nonlocal nonlinear media: exact solutions. Phys Rev E. 2000;63(1):016610.
   Google Scholar
• Zhou Q, Liu L, Zhang H, et al. Dark and singular optical solitons with competing nonlocal nonlinearities. Opt Appl. 46(1).
   Google Scholar
• Podlubny I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. San Diego: Elsevier; 1998.
   Google Scholar
• Li ZB, He JH. Fractional complex transform for fractional differential equations. Math Comput Appl. 2010;15(5):970–973.
   Web of Science ®Google Scholar
• Das A, Ghosh N, Ansari K. Bifurcation and exact traveling wave solutions for dual power Zakharov–Kuznetsov–Burgers equation with fractional temporal evolution. Comput Math Appl. 2017;75:59–69.
   Web of Science ®Google Scholar
• Das A, Ghosh N. Bifurcation of traveling waves and exact solutions of Kadomtsev–Petviashvili modified equal width equation with fractional temporal evolution. Comput Appl Math. 2019;38(1):9.
   Web of Science ®Google Scholar
• Das A, Saha A. Dynamical survey of the dual power Zakharov–Kuznetsov–Burgers equation with external periodic perturbation. Comput Math Appl. 2018;76(5):1174–1183.
   Web of Science ®Google Scholar
• Das A. Explicit Weierstrass traveling wave solutions and bifurcation analysis for dissipative Zakharov–Kuznetsov modified equal width equation. Comput Appl Math. 2018;37(3):3208–3225.
   Web of Science ®Google Scholar
• Guckenheimer J, Holmes P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields/John Guckenheimer, Philip Holmes. New York: Springer-Verlag; 1983.
   Google Scholar
• Liu X, Han M. Bifurcation of periodic solutions and invariant tori for a four-dimensional system. Nonlinear Dyn. 2009;57(1–2):75–83.
   Web of Science ®Google Scholar
• Liu H, Yan F, Xu C. The bifurcation and exact travelling wave solutions of (1+2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity. Nonlinear Dyn. 2012;67(1):465–473.
   Web of Science ®Google Scholar
• Zhong L, Tang S, Qiao L. Bifurcations and exact traveling wave solutions for a class of nonlinear fourth-order partial differential equations. Nonlinear Dyn. 2015;80(1):129–145.
   Web of Science ®Google Scholar
• Li J, Chen G. Bifurcations of traveling wave solutions for four classes of nonlinear wave equations. Int J Bifurcation Chaos. 2005;15(12):3973–3998.
   Web of Science ®Google Scholar
• Zhang Z-f., Ding T-R, Huang W-Z. Qualitative theory of differential equationsState of New Jersey): American Mathematical Society Providence; 1992.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Bin Z. (g'/g)-expansion method for solving fractional partial differential equations in the theory of mathematical physics. Commun Theor Phys. 2012;58(5):623.
   Web of Science ®Google Scholar
• Galvin C. Wave breaking in shallow water, Waves on beaches and resulting sediment transport. 1972;413–456.
   Google Scholar
• Banner M, Peregrine D. Wave breaking in deep water. Annu Rev Fluid Mech. 1993;25(1):373–397.
   Web of Science ®Google Scholar
• Kanel GI, Razorenov SV, Fortov VE. Shock-wave phenomena and the properties of condensed matter. New York: Springer Science & Business Media; 2004.
   Google Scholar
• Feng YL, Shan WR, Sun WR, et al. Bifurcation analysis and solutions of a three-dimensional Kudryashov–Sinelshchikov equation in the bubbly liquid. Commun Nonlinear Sci Numer Simul. 2014;19(4):880–886.
   Web of Science ®Google Scholar
• Kudryashov NA. Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fract. 2005;24(5):1217–1231.
   Web of Science ®Google Scholar
• Vitanov NK, Dimitrova ZI. Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDES from ecology and population dynamics. Commun Nonlinear Sci Numer Simul. 2010;15(10):2836–2845.
   Web of Science ®Google Scholar
• Kudryashov NA, Demina MV. Traveling wave solutions of the generalized nonlinear evolution equations. Appl Math Comput. 2009;210(2):551–557.
   Web of Science ®Google Scholar
• Vitanov NK. Modified method of simplest equation: powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear pdes. Commun Nonlinear Sci Numer Simul. 2011;16(3):1176–1185.
   Web of Science ®Google Scholar
• Vitanov NK. On modified method of simplest equation for obtaining exact and approximate solutions of nonlinear PDES: the role of the simplest equation. Commun Nonlinear Sci Numer Simul. 2011;16(11):4215–4231.
   Web of Science ®Google Scholar