Numerical computation of fractional Kersten-Krasil’shchik coupled KdV-mKdV system occurring in multi-component plasmas

Amit Goswami; Sushila; Jagdev Singh; Devendra Kumar; Amit Goswami; Sushila; Jagdev Singh; Devendra Kumar

doi:10.3934/math.2020155

AIMS Mathematics

2020, Volume 5, Issue 3: 2346-2368. doi: 10.3934/math.2020155

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Numerical computation of fractional Kersten-Krasil’shchik coupled KdV-mKdV system occurring in multi-component plasmas

1.
Department of Physics, Jagan Nath University, Jaipur-303901, Rajasthan, India
2.
Department of Physics, Vivekananda Global University, Jaipur-303012, Rajasthan, India
3.
Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India
4.
Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India

Received: 30 September 2019 Accepted: 07 February 2020 Published: 03 March 2020
MSC : 26A33, 35A22, 35R11, 76X05

In this paper, we study the nonlinear behaviour of multi-component plasma. For this an efficient technique, called Homotopy perturbation Sumudu transform method (HPSTM) is introduced. The power of method is represented by solving the time fractional Kersten-Krasiloshchik coupled KdV-mKdV nonlinear system. This coupled nonlinear system usually arises as a description of waves in multi-component plasmas, traffic flow, electric circuits, electrodynamics and elastic media, shallow water waves etc. The prime purpose of this study is to provide a new class of technique, which need not to use small parameters for finding approximate solution of fractional coupled systems and eliminate linearization and unrealistic factors. Numerical solutions represent that proposed technique is efficient, reliable, and easy to use to large variety of physical systems. This study shows that numerical solutions gained by HPSTM are very accurate and effective for analysis the nonlinear behaviour of system. This study also states that HPSTM is much easier, more convenient and efficient than other available analytical methods.
- Kersten-Krasil’shchik coupled KdV-mKdV system,
- Sumudu transform,
- Homotopy perturbation method,
- He’s polynomials,
- multi-component plasmas
Citation: Amit Goswami, Sushila, Jagdev Singh, Devendra Kumar. Numerical computation of fractional Kersten-Krasil’shchik coupled KdV-mKdV system occurring in multi-component plasmas[J]. AIMS Mathematics, 2020, 5(3): 2346-2368. doi: 10.3934/math.2020155

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Abstract

In this paper, we study the nonlinear behaviour of multi-component plasma. For this an efficient technique, called Homotopy perturbation Sumudu transform method (HPSTM) is introduced. The power of method is represented by solving the time fractional Kersten-Krasiloshchik coupled KdV-mKdV nonlinear system. This coupled nonlinear system usually arises as a description of waves in multi-component plasmas, traffic flow, electric circuits, electrodynamics and elastic media, shallow water waves etc. The prime purpose of this study is to provide a new class of technique, which need not to use small parameters for finding approximate solution of fractional coupled systems and eliminate linearization and unrealistic factors. Numerical solutions represent that proposed technique is efficient, reliable, and easy to use to large variety of physical systems. This study shows that numerical solutions gained by HPSTM are very accurate and effective for analysis the nonlinear behaviour of system. This study also states that HPSTM is much easier, more convenient and efficient than other available analytical methods.

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