Department Of Mathematics And Statistics

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    Highly dispersive W�shaped and other optical solitons with quadratic�cubic nonlinearity: Symmetry analysis and new Kudryashov's method
    (Elsevier Ltd, 2023-06-24T00:00:00) Yadav, Ravindra; Malik, Sandeep; Kumar, Sachin; Sharma, Rajesh; Biswas, Anjan; Y?ld?r?m, Yakup; Gonz�lez-Gaxiola, O.; Moraru, Luminita; Alghamdi, Abdulah A.
    Lie symmetry analysis is utilized in this paper to explore the properties of highly dispersive optical solitons that exhibit quadratic�cubic self-phase modulation. The use of Lie symmetry analysis enables the reduction of the governing partial differential equation to an ordinary differential equation, which is then integrated using an enhanced Kudryashov's approach to obtain solitons with the model. The analysis presented in this paper does not explicitly discuss the formation and dynamics of soliton radiation. � 2023
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    Soliton Solutions of�Dual-mode Kawahara Equation via�Lie Symmetry Analysis
    (Springer Science and Business Media Deutschland GmbH, 2022-06-29T00:00:00) Malik, Sandeep; Kumar, Sachin
    In this article, we investigate a newly proposed dual-mode Kawahara equation. Our main aim in this paper is to find out the soliton and periodic solutions of the Kawahara equation. Initially, we reduce the governing equation into an ordinary differential equation by applying the Lie symmetry analysis. Further, we derive the soliton and periodic solutions via three integration methods, namely sech-csch scheme, exp-expansion method, and modified F-expansion method. � 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
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    The (3 + 1)-dimensional Benjamin-Ono equation: Painlev� analysis, rogue waves, breather waves and soliton solutions
    (World Scientific, 2022-06-08T00:00:00) Kumar, Sachin; Malik, Sandeep
    In this paper, we analyzed the (3 + 1)-dimensional Benjamin-Ono (BO) equation. We first demonstrated that the governing model is not integrable in the Painlev� sense. The rogue wave and the breather wave solutions are then achieved with the use of bilinear form. Furthermore, using a combination of Lie symmetry analysis with the new Kudryshov method, and the Riccati equation technique, the abundant soliton and singular periodic solutions were derived. The criteria for existence of such solutions are also provided. Consequently, the derived solutions are presented graphically through 3D, 2D and contour plots, which describe useful physical phenomena due to existence of the free parameters. Corresponding to the one-reduction, power series solution of BO equation is also obtained. � 2022 World Scientific Publishing Company.
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    Optical solitons and bifurcation analysis in fiber Bragg gratings with Lie symmetry and Kudryashov�s approach
    (Springer Science and Business Media B.V., 2021-06-24T00:00:00) Malik, Sandeep; Kumar, Sachin; Biswas, Anjan; Ekici, Mehmet; Dakova, Anelia; Alzahrani, Abdullah Khamis; Belic, Milivoj R.
    A combination of Lie symmetry analysis and Kudryashov�s approach secures optical soliton solutions with fiber Bragg gratings. The bifurcation analysis is carried out, and the phase portrait is presented. � 2021, The Author(s), under exclusive licence to Springer Nature B.V.