Optical solitons with complex Ginzburg-Landau equation by modified simple equation method

Abstract This paper applied the modified simple equation method to complex Ginzburg–Landau equation to secure soliton solutions. Both Kerr and power laws of nonlinearity are studied. These soliton solutions appear with a couple of constraints and guarantees their existence.

[1]  F. Tchier,et al.  Optical solitons of the coupled nonlinear Schrödinger’s equation with spatiotemporal dispersion , 2016 .

[2]  F. Tchier,et al.  On soliton structures of generalized resonance equation with time dependent coefficients , 2017 .

[3]  Shou-Fu Tian,et al.  Rogue waves, homoclinic breather waves and soliton waves for the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation , 2017, Appl. Math. Lett..

[4]  Sahay Shwetanshumala,et al.  Temporal Solitons of Modified Complex Ginzberg Landau Equation , 2008 .

[5]  D. Baleanu,et al.  Optical solitons of transmission equation of ultra-short optical pulse in parabolic law media with the aid of Backlund transformation , 2017 .

[6]  Timoleon Crepin Kofane,et al.  Dissipative optical bullets modeled by the cubic-quintic-septic complex Ginzburg-Landau equation with higher-order dispersions , 2017, Commun. Nonlinear Sci. Numer. Simul..

[7]  Shou-Fu Tian,et al.  On the integrability of a generalized variable-coefficient Kadomtsev–Petviashvili equation , 2011, 1112.1499.

[8]  A. Yusuf,et al.  Dark optical, singular solitons and conservation laws to the nonlinear Schrödinger’s equation with spatio-temporal dispersion , 2017 .

[9]  M. Belić,et al.  Soliton solutions to resonant nonlinear schrodinger's equation with time-dependent coefficients by modified simple equation method , 2016 .

[10]  Shou-Fu Tian,et al.  On periodic wave solutions with asymptotic behaviors to a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid dynamics , 2016, Comput. Math. Appl..

[11]  A. Biswas,et al.  Optical solitons in birefringent fibers with modified simple equation method , 2017 .

[12]  Buyang Li,et al.  Global well-posedness of the time-dependent Ginzburg-Landau superconductivity model in curved polyhedra , 2014, 1411.4235.

[13]  Shou-Fu Tian,et al.  Riemann theta functions periodic wave solutions and rational characteristics for the nonlinear equations , 2010 .

[14]  M. Belić,et al.  Optical solitons with complex Ginzburg–Landau equation , 2016 .

[15]  Bulent Kilic,et al.  Soliton solutions for the Kundu–Eckhaus equation with the aid of unified algebraic and auxiliary equation expansion methods , 2016 .

[16]  F. Tchier,et al.  Nanoscale Waveguides in Optical Metamaterials: Jacobi Elliptic Funtion Solutions , 2017 .

[17]  F. Tchier,et al.  On optical solitons of the Schrödinger-Hirota equation with power law nonlinearity in optical fibers , 2017 .

[18]  D. Baleanu,et al.  On combined optical solitons of the one-dimensional Schrödinger’s equation with time dependent coefficients , 2016 .

[19]  A. Biswas,et al.  Optical solitons in nonlinear directional couplers with trial function scheme , 2017 .

[20]  Shou-Fu Tian,et al.  Initial–boundary value problems for the general coupled nonlinear Schrödinger equation on the interval via the Fokas method☆ , 2017 .

[21]  Shou-Fu Tian,et al.  Dynamics of the breathers, rogue waves and solitary waves in the (2+1)-dimensional Ito equation , 2017, Appl. Math. Lett..

[22]  Shou-Fu Tian,et al.  Conservation laws, bright matter wave solitons and modulational instability of nonlinear Schrödinger equation with time-dependent nonlinearity , 2012, 1201.1145.

[23]  F. Tchier,et al.  Optical solitons in parabolic law medium: Jacobi elliptic function solution , 2016 .

[24]  Shou-Fu Tian,et al.  The mixed coupled nonlinear Schrödinger equation on the half-line via the Fokas method , 2016, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[25]  A. Biswas,et al.  Soliton solutions to resonant nonlinear Schrödinger’s equation with time-dependent coefficients by trial solution approach , 2015 .

[26]  Z. Korpinar,et al.  Approximate solutions of bright and dark optical solitons in birefrigent fibers , 2017 .

[27]  M. Inç,et al.  Compact and non compact structures of the phi-four equation , 2017 .

[28]  Anjan Biswas,et al.  TEMPORAL 1-SOLITON SOLUTION OF THE COMPLEX GINZBURG-LANDAU EQUATION WITH POWER LAW NONLINEARITY , 2009 .

[29]  Hongqing Zhang,et al.  Analytic solutions, Darboux transformation operators and supersymmetry for a generalized one-dimensional time-dependent Schrödinger equation , 2012, Appl. Math. Comput..

[30]  Shou-Fu Tian,et al.  Bäcklund transformation, infinite conservation laws and periodic wave solutions to a generalized (2+1)-dimensional Boussinesq equation , 2016 .

[31]  Bulent Kilic.  Optical solitons for the Schrödinger-Hirota equation with power law nonlinearity by the Bäcklund transformation , 2017 .

[32]  Abdullahi Yusuf,et al.  Optical and other solitons for the fourth-order dispersive nonlinear Schrödinger equation with dual-power law nonlinearity , 2017 .

[33]  Shou-Fu Tian,et al.  On integrability and quasi-periodic wave solutions to a (3+1)-dimensional generalized KdV-like model equation , 2016, Appl. Math. Comput..

[34]  M. Belić,et al.  Dark and singular optical solitons with spatio-temporal dispersion using modified simple equation method , 2017 .

[35]  Abdelkader Aissat,et al.  A geo-numerical approach for the classification of fixed points in the reduced model of the cubic-quintic complex Ginzburg-Landau equation , 2015 .

[36]  M. Belić,et al.  Solitons in Optical Metamaterials with Trial Solution Approach and Bäcklund Transform of Riccati Equation , 2015 .

[37]  Necdet Bildik.  Non - Perturbative Solution of the Ginzburg - Landau Equation , 2000 .