Monisha, S and Vishnu Priya, N and Senthilvelan, M and Rajasekar, S (2022) Higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity. In: Chaos, Solitons and Fractals, 162 .
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Abstract
We construct certain higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity. We utilize the generalized Darboux transformation method to construct the aforementioned solutions. The three well-known equations, namely nonlinear Schrödinger equation, Hirota equation, and generalized nonlinear Schrödinger equation, are sub-cases of the considered extended nonlinear Schrödinger equation. The solutions which we construct are more general. We analyze how the positon and breather positon solutions of the constituent equations get modified by the higher order nonlinear and dispersion terms. Our results show that the width and direction of the smooth positon and breather-positon solutions are highly sensitive to higher-order effects. Further, we carry out an asymptotic analysis to predict the behaviour of positons. We observe that during collision positons exhibit a time-dependent phase shift. We also present the exact expression of time-dependent phase shift of positons. Finally, we show that this time-dependent phase shift is directly proportional to the higher order nonlinear and dispersion parameters.
| Item Type: | Journal Article |
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| Publication: | Chaos, Solitons and Fractals |
| Publisher: | Elsevier Ltd |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Control nonlinearities; Dispersions; Mathematical transformations; Nonlinear equations, Darboux transformation method; Generalized darboux transformation method; High order nonlinear schrödinge equation; High-order; High-order smooth; Higher-order; Hirota equation; Positon solution; Positons; Time dependent, Asymptotic analysis |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 27 Aug 2022 09:24 |
| Last Modified: | 27 Aug 2022 09:24 |
| URI: | https://eprints.iisc.ac.in/id/eprint/76265 |
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