On the modified Gardner type equation and its time fractional form

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-PastaUlam (FPU) model, and found that these two equations are related with nonlinear Schrospacing diaeresis dinger equation (NLS) type of equations. Subsequently, symmetries and conservation laws are investigated. Finally, Ba spacing diaeresis 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 Schrospacing diaeresis dinger equation. Another key point is that Ba spacing diaeresis 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. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

Differential equations play a vital role in scientific research. This article focuses on the modified Gardner-type equation and its time fractional form, deriving them from the Fermi-Pasta-Ulam model and establishing their connection with the nonlinear Schroedinger equation. The study also investigates symmetries, conservation laws, and presents the Baclund transformation of conservation laws.