Optical soliton solutions of the resonant nonlinear Schrödinger equation with Kerr-law nonlinearity

M. Justin, M.B. Hubert, G. Betchewe, S.Y. Doka, K.T. Crepin, Chirped solitons in derivative nonlinear Schrödinger equation. Chaos. Solitons Fract. 107, 49–54 (2018)

Article  ADS  Google Scholar 

G.P. Agrawal, Nonlinear Fiber Optics, Nonlinear Science at the Dawn of the 21st Century (Springer, Berlin, Heidelberg, 2020)

Google Scholar 

C. De Angelis, Nonlinear optics. Front. Photonics 1, 628215 (2021)

Article  Google Scholar 

A. Bansal, A. Biswas, Q. Zhou, M.M. Babatin, Lie symmetry analysis for cubic-quartic nonlinear Schrödinger’s equation. Optik 169, 12–15 (2018)

Article  Google Scholar 

K.S. Al-Ghafri, E.V. Krishnan, A. Biswas, Cubic-quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas-Lenells equation. J. Eur. Opt. Society-Rapid Publ. 18, 1–10 (2022)

Article  Google Scholar 

L. Tang, Bifurcations and optical solitons for the coupled nonlinear Schrödinger equation in optical fiber Bragg gratings. J. Opt. 52, 1388–1398 (2023)

Article  Google Scholar 

S. Akrama, J. Ahmada, N.B. Turkib, N.A. Shah, On the exploration of soliton solutions of the nonlinear Manakov system and its sensitivity analysis. Results Phys. 52, 106772 (2023)

Article  Google Scholar 

A. Biswas, M. Mirzazadeh, M. Eslami, D. Milovic, M. Belic, Solitons in optical metamaterials by functional variable method and first integral approach. Frequenz 68, 525–530 (2014)

Article  ADS  Google Scholar 

M. Eslami, M. Mirzazadeh, B.F. Vajargah, A. Biswas, Optical solitons for the resonant nonlinear Schrödinger’s equation with time-dependent coefficients by the first integral method. Opt. Int. J. Light Electron Opt. 125, 3107–3116 (2014)

Article  Google Scholar 

M. Eslami, H. Rezazadeh, The first integral method for Wu-Zhang system with conformable time-fractional derivative. Calcolo 53, 475–485 (2016)

Article  MathSciNet  Google Scholar 

Q. Zhou, M. Ekici, A. Sonmezoglu, M. Mirzazadeh, M. Eslami, Optical solitons with Biswas-Milovic equation by extended trial equation method. Nonlinear Dyn. 84, 1883–1900 (2016)

Article  MathSciNet  Google Scholar 

A. Chowdury, D.J. Kedziora, A. Ankiewicz, N. Akhmediev, Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms. Phys. Rev. E 90, 032922 (2014)

Article  ADS  Google Scholar 

A. Bansal, A. Biswas, H. Triki, Q. Zhou, S.P. Moshokoa, M. Belic, Optical solitons and group invariant solutions to Lakshmanan-Porsezian-Daniel model in optical fibers and PCF. Optik 160, 86–91 (2018)

Article  Google Scholar 

A. Jawad, A. Biswas, Solutions of resonant nonlinear Schrödinger’s equation with exotic non-Kerr law nonlinearities. Rafidain J. Eng. Sci. 2, 43–50 (2024)

Google Scholar 

E.M.E. Zayed, R.M.A. Shohib, M.E.M. Alngar, A. Biswas, Y. Yildirim, A. Asiri, Optical solitons with DWDM topology having parabolic law nonlinearity with multiplicative white noise. J. Opt 53, 2322–2330 (2024)

Article  Google Scholar 

J.V. Guzman, R.T. Alqahtani, Q. Zhou, M.F. Mahmood, S.P. Moshokoa, M.Z. Ullah, A. Biswas, M. Belic, Optical solitons for Lakshmanan-Porsezian-Daniel model with spatio-temporal dispersion using the method of undetermined coefficients. Optik 144, 115–123 (2017)

Article  ADS  Google Scholar 

A. Biswas, Y. Yildirim, E. Yasar, Q. Zhou, S.P. Moshokoa, M. Belic, Optical solitons for Lakshmanan-Porsezian-Daniel model by modified simple equation method. Optik 160, 24–32 (2018)

Article  Google Scholar 

A.A. Al Qarni, A.M. Bodaqah, A.S.H.F. Mohammed, A.A. Alshaery, H.O. Bakodah, A. Biswas, Cubic-quartic optical solitons obtained with the Lakshmanan-Porsezian-Daniel equation by an improved Adomian decomposition scheme. Ukr. J. Phys. Opt. 23, 228–242 (2022)

Article  Google Scholar 

M. Savescu, K.R. Khan, P. Naruka, H. Jafari, L. Moraru, A. Biswas, Optical solitons in photonic nano wave guides with an improved nonlinear Schrödinger’s equation. J. Comput. Theor. Nanosci. 10(5), 1182–1191 (2013)

Article  Google Scholar 

M.B. Hubert, G. Betchewe, M. Justin, S.Y. Doka, K.T. Crepin, A. Biswas, Q. Zhou, A.S. Alshomrani, M. Ekici, S.P. Moshokoa, M. Belic, Optical solitons with Lakshmanan-Porsezian-Daniel model by modified extended direct algebraic method. Optik 162, 228–236 (2018)

Article  Google Scholar 

S.N. Chow, J.K. Hale, Method of Bifurcation Theory (Springer, New York, 1982)

Book  Google Scholar 

J. Li, Z. Qiao, Peakon, pseudo-peakon, and cuspon solutions for two generalized Cammasa-Holm equations. J. Math. Phys. 54(12), 123501 (2013)

Article  ADS  MathSciNet  Google Scholar 

J. Li, W. Zhou, G. Chen, Understanding peakons, periodic peakons and compactons via a shallow water wave equation. Int. J. Bifurc. Chaos 26(12), 1650207 (2016)

Article  MathSciNet  Google Scholar 

T.D. Leta, W. Liu, A.E. Achab, H. Rezazadeh, A. Bekir, Dynamical behavior of traveling wave solutions for a \((2+1)\)-dimensional Bogoyavlenskii coupled system. Qual. Theory Dyn. Syst. 20, 14 (2021)

Article  MathSciNet  Google Scholar 

T.D. Leta, J. Li, Various exact soliton solutions and bifurcations of a generalized Dullin-Gottwald-Holm equation with a power law nonlinearity. Int. J. Bifurc. Chaos 27(8), 1750129 (2017)

Article  MathSciNet  Google Scholar 

T.D. Leta, J. Li, Dynamical behavior of traveling wave solutions of a long waves-short waves resonance model. Qual. Theory Dyn. Syst. 18(3), 741–760 (2019)

Article  MathSciNet  Google Scholar 

P. Rosenau, Nonlinear dispersion and compact structures. Phys. Rev. Lett. 73(13), 1737–1741 (1994)

Article  ADS  MathSciNet  Google Scholar 

A.S. Fokas, On a class of physically important integrable equations. Phys. D 87(1–4), 145–150 (1995)

Article  MathSciNet  Google Scholar 

P. Rosenau, On nonanalytic solitary wave formed by a nonlinear dispersion. Phys. Lett. A 230(5–6), 305–318 (1997)

Article  ADS  MathSciNet  Google Scholar 

P. Rosenau, On a class of nonlinear dispersive dissipative interaction. Phys. D 123(1–4), 525–546 (1998)

Article  MathSciNet  Google Scholar 

P. Rosenau, Compact and noncompact dispersive patterns. Phys. Lett. A 275(3), 193–203 (2000)

Article  ADS  MathSciNet  Google Scholar 

A.M. Wazwaz, The tanh-coth and the sine-cosine methods for kinks, solitons, and periodic solutions for the Pochhammer-Chree equations. Appl. Math. Comput. 195, 24–33 (2008)

MathSciNet  Google Scholar 

M. Yaghobi Moghaddam, A. Asgari, H. Yazdani, Exact travelling wave solutions for the generalized nonlinear Schrödinger (GNLS) equation with a source by extended tanh-coth, sine-cosine and Exp-function methods. Appl. Math. Comput. 210, 422–435 (2009)

MathSciNet  Google Scholar 

Z. Yang, Y.C. Benny-Hon, An improved modified extended tanh-function method. Zeitschrift für Naturforschung A 61, 3–4 (2006)

Article  ADS  Google Scholar 

S.A. Elwakil, S.K. El-Labany, M.A. Zahran, R. Sabry, Modified extended tanh-function method and its applications to nonlinear equations. Appl. Math. Comput. 161, 403–412 (2005)

MathSciNet  Google Scholar 

D. Wang, H.-Q. Zhang, Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation. Chaos. Solitons Fract. 25, 601–610 (2005)

Article  ADS  MathSciNet  Google Scholar 

J. Liu, K. Yang, The extended F-expansion method and exact solutions of nonlinear PDEs. Chaos. Solitons Fract. 22, 111–121 (2004)

Article  ADS  MathSciNet  Google Scholar 

M. Wang, X. Li, Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation. Chaos. Solitons Fract. 24, 1257–1268 (2005)

Article  ADS  MathSciNet  Google Scholar 

J.L. Zhang, M.L. Wang, Y.M. Wang, Z.D. Fang, The improved F-expansion method and its applications. Phys. Lett. A 350, 103–109 (2006)

Article  ADS  Google Scholar 

P.F. Byrd, M.D. Fridman, Handbook of Elliptic Integrals for Engineers and Scientists (Springer-Verge, Berlin, 1971)

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