Optical soliton perturbation with quadratic-cubic nonlinearity by mapping methods
Introduction
Optical soliton perturbation with quadratic–cubic (QC) nonlinearity is one of the latest areas of research in the field of fiber–optic telecommunication engineering [1], [2], [3], [4], [5], [6], [9], [13], [14]. The governing model is the nonlinear Schrödinger’s equation (NLSE) that is considered with QC nonlinearity. This kind of non-Kerr type nonlinearity first appeared in 1994 [5] and was again revisited during 2011 [4]. The study of optical solitons with such nonlinear medium has gained popularity ever since. A deluge of results with this form of nonlinearity have been reported. The model was also studied with fractional temporal evolution to minimize the effect of Internet bottleneck [13]. The conservation laws for this model has also been found [14]. Some works on soliton and other solutions can also be found in [16], [17], [18], [19], [20]. This paper will study the perturbed NLSE with QC nonlinearity by the aid of mapping methods. This integration methodology has been successfully applied in the past to water wave problems and other models [7], [8], [10], [11], [12]. There are various other popular schemes to study such nonlinear evolution equations [15]. This scheme will reveal bright, dark and singular soliton solutions to the model. The details are now presented in the rest of the paper.
Section snippets
Governing model
The equation under consideration isIn (1), u(x, t) stands for the complex valued wave profile with two independent variables x and t which respectively denote spatial and temporal components. First term in (1) is the linear evolution, a is the coefficient of group velocity dispersion (GVD), b1 and b2 indicate the coefficients of the quadratic and cubic nonlinearity terms respectively. On the right hand side of (1), term with α is intermodal
Conclusions
Three forms of mapping methods retrieved bright, dark and singular soliton solutions to the perturbed NLSE with QC nonlinearity. The regular mapping method, modified mapping method and extended mapping method yielded these soliton solutions. These integration schemes directly retrieved solutions in terms of JEFs and in the limiting case, soliton solutions were revealed. These are all listed along with constraint relations on the parameters that guarantee the existence of these solutions. The
Conflict of interest
The authors also declare that there is no conflict of interest.
Acknowledgements
This work of Qin Zhou was supported by the National Natural Science Foundation of China (Grant Nos. 11705130 and 11547149), this author was also sponsored by the Chutian Scholar Program of Hubei Government in China. The research work of sixth author (MRB) was supported by the grant number NPRP 8-028-1-001 and is thankful for it.
References (20)
- et al.
Resonant optical solitons with quadratic–cubic nonlinearity by semi–inverse variational principle
Optik (Stuttg)
(2017) - et al.
Optical solitons in nonlinear negative-index materials with quadratic–cubic noinlinearity
Superlattices Microstruct.
(2017) - et al.
Optical solitons with modified extended algebraic method for quadratic–cubic nonlinearity
Optik
(2018) - et al.
Optical soliton perturbation with quadratic–cubic nonlinearity by riccati- bernoulli sub–ODE method and kudryashov’s scheme
Optik
(2017) - et al.
Mitigating internet bottleneck with fractional temporal evolution of optical solitons having quadratic–cubic nonlinearity
Optik (Stuttg)
(2018) - et al.
Optical solitons and conservation laws with quadratic–cubic nonlinearity
Optik (Stuttg)
(2017) The integrable vakhnenko–parkes (VP) and the modified vakhnenko–parkes (MVP) equations: multiple real and complex soliton solutions
Chin. J. Phys.
(2019)- et al.
Dynamics of one-dimensional quantum droplets
Phys. Rev. A
(2018) - et al.
Chaotic solitons in the quadratic–cubic nonlinear schrödinger equation under nonlinearity management
Chaos
(2011) - et al.
Prediction of unique solitary–wave polaritons in quadratic–cubic nonlinear dispersive media
J. Optical Soc. Am. B
(1994)
Cited by (14)
Solitons and conservation laws in magneto–optic waveguides with generalized Kudryashov's equation
2021, Chinese Journal of PhysicsCubic-quartic optical solitons with Kudryashov's law of refractive index by F-expansions schemes
2020, Results in PhysicsCitation Excerpt :The theory of optical solitons has made remarkable and far-reaching advances during the past few decades [1–50].
Optical solitons in fiber Bragg gratings having Kerr law of refractive index with extended Kudryashov's method and new extended auxiliary equation approach
2020, Chinese Journal of PhysicsCitation Excerpt :Such studies are all under way and their results are on the horizon. Additional mathematical tool that have been successfully implemented in this field of research will later recover novel results [34–43]. Such studies are under way and these results are a short while away from its visibility.
Optical solitons with Kudryashov's model by a range of integration norms
2020, Chinese Journal of PhysicsPeriodic and solitary waves in optical fiber Bragg gratings with dispersive reflectivity
2020, Chinese Journal of PhysicsCitation Excerpt :In this regard, many researchers try to find soliton solutions directly using various special methods. In paper [9] soliton solutions were found for the perturbed nonlinear Schrödinger equation that was studied with quadratic-cubic nonlinearity by means of the mapping methods. The bright, dark and singular optical soliton solutions were found in Arnous et al. [10] to the nonlinear Schrödinger’s equation for anti-cubic nonlinearity by extended direct algebraic method.