Abstract

By using the lens-type transformation, exact soliton and quasi-soliton similaritons are found in (1+1), (2+1) and (3+1)-dimensional nonlinear Schrödinger equations in the context of nonlinear optical fiber amplifiers and graded-index waveguide amplifiers. The novel analytical and numerical results show that, in addition to the exact solitonic optical waves, quasi-solitonic optical waves with Gaussian, parabolic, vortex and ring soliton profiles can evolve exact self-similarly without any radiation.

Highlights

  • The nonlinear Schrodinger equation (NLSE) and its stationary solutions, such as solitons and vortices, have been extensively studied in various fields such as nonlinear optical systems, plasmas, fluid dynamics, Bose-Einstein condensation and condensed matter physics

  • The concept of self-similar evolution of parabolic pulses was transplanted to the context of nonlinear planar waveguide amplifiers where the asymptotic parabolic similaritons were found for (1+1)-dimensional NLSE and for (2+1)-dimensional NLSE [5]

  • The other important aspect of this paper is to report the existence of exact optical similaritons in these higher dimensional NLSEs

Read more

Summary

Introduction

The nonlinear Schrodinger equation (NLSE) and its stationary solutions, such as solitons and vortices, have been extensively studied in various fields such as nonlinear optical systems, plasmas, fluid dynamics, Bose-Einstein condensation and condensed matter physics. Only a few results have been reported about exact optical similaritons described by the quasi-soliton solutions in dispersionmanaged optical fibers [21, 22]. Such kind of exact quasi-soliton similariton has more attractive properties than those of the soliton because of its reduced interaction and smaller peak power than the soliton [21] and allows a possible pedestal-free pulse compression [22]. The prime aspect of this paper is to seek the exact optical similaritons, other than those with sech or tanh-type profile, under the dispersion, nonlinearity and amplification management.

Model equations
Spatial similaritons
Conclusion

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.