Abstract
In this paper, the resonant nonlinear Schrödinger’s equation is studied with four forms of nonlinearity and time-dependent coefficients. The trial solution method is employed to solve the governing equations. Solitons and singular periodic solutions are obtained. The constraint conditions naturally emerge from the solution structure that are needed for its existence.
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Biswas, A.: Soliton solutions of the perturbed resonant nonlinear dispersive Schrödinger’s equation with full nonlinearity by semi-inverse variational principle. Quantum Phys. Lett. 1(2), 79–84 (2012)
Bulut, H., Pandir, Y., Demiray, S.T.: Exact solutions of nonlinear Schrödinger’s equation with dual power-law nonlinearity by extended trial equation method. Waves Random Complex Media 24(4), 439–451 (2014)
Eslami, M., Mirzazadeh, M., Biswas, A.: Soliton solutions of the resonant nonlinear Schrödinger’s equation in optical fibers with time dependent coefficients by simplest equation approach. J. Mod. Optics. 60(19), 1627–1636 (2013)
Eslami, M., Mirzazadeh, M., Vajargah, B.F., Biswas, A.: Optical solitons for the resonant nonlinear Schrödinger’s equation with time-dependent coefficients by the first integral method. Optik 125(9), 3107–3116 (2014)
Geng, X., Lv, Y.: Darboux transformation for an integrable generalization of the nonlinear Schrödinger equation. Nonlinear Dyn. 69(4), 1621–1630 (2012)
Gupta, R.K., Bansal, A.: Similarity reductions and exact solutions of Bretherton equation with time-dependent coefficients. Nonlinear Dyn. 71(1), 1–12 (2013)
Gupta, R.K., Kumar, V., Jiwari, R.: Exact and numerical solutions of coupled short pulse equation with time-dependent coefficients. Nonlinear Dyn. 79(1), 455–464 (2015)
Gurefe, Y., Sonmezoglu, A., Misirli, E.: Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics. Pramana 77, 1023–1029 (2011)
Krishnan, E.V., Kumar, S., Biswas, A.: Solitons and other nonlinear waves of Boussinesq equation. Nonlinear Dyn. 70(2), 1213–1221 (2012)
Liu, C.S.: Trial equation method to nonlinear evolution equations with rank inhomogeneous: mathematical discussions and its applications. Commun. Theor. Phys. 45, 219–223 (2006)
Mirzazadeh, M., Eslami, M., Milovic, D., Biswas, A.: Topological solitons of resonant nonlinear Schrödinger’s equation with dual-power law nonlinearity using \(G^{\prime }/G\)-expansion technique. Optik 125(19), 5480–5489 (2014)
Mirzazadeh, M., Eslami, M., Vajargah, B.F., Biswas, A.: Optical solitons and optical rogons of generalized resonant dispersive nonlinear Schrödinger’s equation with power law nonlinearity. Optik 125(9), 4246–4256 (2014)
Rui, C., Jian, Z.: Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient. Chin. Phys. B 22(10), 100507 (2013)
Triki, H., Hayat, T., Aldossary, O.M., Biswas, A.: Bright and dark solitons for the resonant nonlinear Schrödinger’s equation with time- dependent coefficients. Opt. Laser Technol. 44, 2223–2231 (2012)
Triki, H., Yildirim, A., Hayat, T., Aldossary, O.M., Biswas, A.: 1-soliton solution of the generalized resonant nonlinear dispersive Schrödinger’s equation with time-dependent coefficients. Adv. Sci. Lett. 16, 309–312 (2012)
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Mirzazadeh, M., Arnous, A.H., Mahmood, M.F. et al. Soliton solutions to resonant nonlinear Schrödinger’s equation with time-dependent coefficients by trial solution approach. Nonlinear Dyn 81, 277–282 (2015). https://doi.org/10.1007/s11071-015-1989-1
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DOI: https://doi.org/10.1007/s11071-015-1989-1