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
Summary
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.
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