Exact analytic solitary wave solutions for the RKL model. (English) Zbl 1186.35210

Triki, Houria; Taha, Thiab R.

Math. Comput. Simul. 80, No. 4, 849-854 (2009).

Summary: Interest in finding exact solitary wave solutions of nonlinear evolution equations by means of different methods has grown steadily in recent years. These exact solutions are important to understand the mechanism of the complicated nonlinear physical phenomena. By use of the Jacobi elliptic function method, we find the exact analytic solitary wave solutions for the RKL model with cubic-quintic non-Kerr terms, describing the propagation of extremely short pulses in optical fibers. These new solutions may be useful for describing the propagation of optical pulses in non-Kerr media.

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
35Q51	Soliton equations
35C08	Soliton solutions
35C05	Solutions to PDEs in closed form
78A10	Physical optics

Keywords:

non-Kerr medium; exact analytic solutions; Jacobi elliptic function method

References:

[1]	Du, M.; Chan, A. K.; Chui, C. K., A novel approach to solving the nonlinear Schrödinger equation by the coupled amplitude-phase formulation”, IEEE J. Quant. Electron., 31, 1, 177-182 (1995)
[2]	El-Wakil, S. A.; Abdou, M. A.; Elhanbaly, A., New solitons and periodic wave solutions for nonlinear evolution equations, Phys. Lett. A, 353, 40-47 (2006) · Zbl 1106.65115
[3]	Frantzeskakis, D. J.; Hizanidis, K.; Tombras, G. S.; Belia, I., Nonlinear dynamics of femtosecond optical solitary wave at the zero dispersion point, IEEE J. Quant. Electron., 31, 1, 183-189 (1995)
[4]	Gedalin, M.; Scott, T. C.; Band, Y. B., Optical solitary waves in the higher order nonlinear Schrödinger equation, Phys. Rev. Lett., 78, 3, 448-451 (1997)
[5]	Hong, W.-P., Optical solitary wave solutions for the higher order nonlinear Schrödinger equation with cubic-quintic non-Kerr terms, Opt. Commun., 194, 217-223 (2001)
[6]	Li, Z.; Li, Lu; Tian, H.; ZhouF G., New types of solitary wave solutions for the higher order nonlinear Schrödinger equation, Phys. Rev. Lett., 84, 18, 4096-4099 (2000)
[7]	Li, X.; Wang, M., A sub-ODE method for finding exact solutions of a generalized KdV-mKdV equation with high- order nonlinear terms, Phys. Lett. A, 361, 115-118 (2007) · Zbl 1170.35085
[8]	Palacios, S. L., Two simple ansätze for obtaining exact solutions of high dispersive nonlinear Schrödinger equations, Chaos Solitons Fractals, 19, 203-207 (2004) · Zbl 1092.35526
[9]	Palacios, S. L.; Fernandez-Diaz, J. M., Black optical solitons for media with parabolic nonlinearity law in the presence of fourth order dispersion, Opt. Commun., 178, 457-460 (2000)
[10]	Radhakrishnan, R.; Kundu, A.; Lakshmanan, M., Coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity: integrability and soliton interaction in non-Kerr media, Phys. Rev. E, 60, 3, 3314-3323 (1999)
[11]	Triki, H.; El Akrmi, A.; Rabia, M. K., Soliton solutions in three linearly coupled Korteweg—de Vries equations, Opt. Commun., 201, 447-455 (2002)
[12]	Turitsyn, S. K.; Shapiro, E. G.; Medvedev, S. B.; Fedoruk, M. P.; Mezentsev, V. K., Physics and mathematics of dispersion-managed optical solitons, C. R. Phys., 4, 145-161 (2003)
[13]	Wang, M.; Li, X.; Zhang, J., Sub-ODE method and solitary wave solutions for higher order nonlinear Schrödinger equation, Phys. Lett. A, 363, 96-101 (2007) · Zbl 1197.81129
[14]	Zayed, E. M.E.; Zedan, H. A.; Gepreel, K. A., On the solitary wave solutions for nonlinear Hirota-satsuma coupled KdV of equations, Chaos Solitons Fractals, 22, 285-303 (2004) · Zbl 1069.35080
[15]	Zhang, J.; Dai, C., Bright and dark optical solitons in the nonlinear Schrödinger equation with fourth-order and cubic-quintic nonlinearity, Chin. Opt. Lett., 3, 5, 295-298 (2005)
[16]	Zhang, J.-L.; Wang, M.-L.; Li, X.-Z., The subsidiary ordinary differential equations and the exact solutions of the higher order dispersive nonlinear Schrödinger equation, Phys. Lett. A, 357, 188-195 (2006) · Zbl 1236.81092
[17]	Zhu, S.-D., Exact solutions for the high-order dispersive cubic-quintic nonlinear Schrodinger equation by the extended hyperbolic auxiliary equation method, Chaos Solitons Fractals, 34, 1608-1612 (2007) · Zbl 1152.35502