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Chirped Optical Solitons in Birefringent Fibers with Parabolic Law Nonlinearity and Four-Wave Mixing

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Triki H., Biswas A., Milović D., Belić M.

Acta Physica Polonica A

2016

vol. 130

issue 3

718-726

We investigate exact soliton solutions with nonlinear chirp for the coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity, self-steepening, self-frequency shift and four-wave mixing. The model governs the femtosecond pulse propagation in birefringent fibers. We introduce a new ansatz to obtain the nonlinear chirp associated with the propagating soliton pulses. New chirped soliton pair solutions with non-trivial chirping are found for the coupled nonlinear equations, illustrating the potentially rich set of solitonic pulse solutions of the model with higher-order effects. The solutions comprise two types of bright-W-shaped and bright-bright soliton pairs as well as kink and anti-kink pulses. Interestingly, the bright wave in the bright-W shaped soliton pairs possesses a platform underneath it, originating from the self-steepening and self-frequency shift effects. The corresponding chirp associated with each of these optical soliton pairs is also determined. It is shown that the nonlinear chirp is related to the pair intensity and determined by self-frequency shift and pause self-steepening. Parametric conditions for the existence and uniqueness of chirped solutions are given.

Soliton Solution and Conservation Law of Gear-Grimshaw Model for Shallow Water Waves

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Triki H., Kara A., Bhrawy A., Biswas A.

vol. 125

issue 5

1099-1107

This paper is going to obtain the soliton solution of the Gear-Grimshaw model that describes the dynamics of two-layered shallow water waves in oceans and rivers. The topological 1-soliton solution will be obtained by the ansatz method. There are several constraint conditions that will be taken care of. This will be followed by the model with power law nonlinearity. Subsequently, the conservation laws for this model will be derived by the aid of multiplier approach from the Lie symmetry analysis. Finally, the F-expansion method will extract a few more interesting solutions to the model.

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2 Acta Physica Polonica A

1 2016

1 2014

2 Biswas A.

2 Triki H.

1 Belić M.

1 Bhrawy A.

1 Kara A.

1 Milović D.

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Chirped Optical Solitons in Birefringent Fibers with Parabolic Law Nonlinearity and Four-Wave Mixing

Soliton Solution and Conservation Law of Gear-Grimshaw Model for Shallow Water Waves