A NEW (3+1)-DIMENSIONAL KDV EQUATION AND MKDV EQUATION WITH THEIR CORRESPONDING FRACTIONAL FORMS

Gangwei Wang and Abdul-Majid Wazwaz
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Gangwei Wang: School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, P. R. China
Abdul-Majid Wazwaz: ��Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA

FRACTALS (fractals), 2022, vol. 30, issue 04, 1-8

Abstract: In this work, new (3+1)-dimensional Korteweg–de Vries (KdV) equation and modified KdV (mKdV) equation as well as the corresponding fractional forms are presented. These two equations are derived for the first time relying on the extended (3+1)-dimensional zero curvature equation. In addition, symmetries and conservation laws are displayed. Meanwhile, one-soliton solution for the time fractional of (3+1)-dimensional KdV equation and mKdV equation is obtained.

Keywords: KdV Equation and mKdV Equation; Zero Curvature Equation; Group Invariant Solutions; Symmetries and Conservation Laws; Soliton Solutions (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500815

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