On the modified Gardner type equation and its time fractional form

Gangwei Wang and Abdul-Majid Wazwaz

Chaos, Solitons & Fractals, 2022, vol. 155, issue C

Abstract: Differential equations play an important role in many scientific fields. In this work, we study modified Gardner-type equation and its time fractional form. We first derive these two equations from Fermi-Pasta-Ulam (FPU) model, and found that these two equations are related with nonlinear Schro¨dinger equation (NLS) type of equations. Subsequently, symmetries and conservation laws are investigated. Finally, Ba¨cklund transformation of conservation laws also presented. In this article, we not only derive these two equations, but also use perturbation analysis to find the connection between them and the Schro¨dinger equation. Another key point is that Ba¨cklund transformation of conservation laws are also obtained. From these results, it is obvious that the Lie group method is a very effective method for dealing with partial differential equations.

Keywords: Modified Gardner-type equation; Perturbation and symmetry analysis; Ba¨cklund transformation; Conservation laws (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010481

DOI: 10.1016/j.chaos.2021.111694

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