GROUP ANALYSIS OF THE TIME FRACTIONAL (3 + 1)-DIMENSIONAL KDV-TYPE EQUATION
Jian‐Gen Liu, Xiao‐Jun Yang, Lu‐Lu Geng, Yu-Rong Fan
Abstract
Under investigations into this paper is a higher-dimensional model, namely the time fractional [Formula: see text]-dimensional Korteweg–de Vries (KdV)-type equation, which can be usually used to express shallow water wave phenomena. At the beginning, the symmetry of the time fractional [Formula: see text]-dimensional KdV-type equation via the group analysis scheme is obtained. The definition of the fractional derivative in the sense of the Riemann–Liouville is considered. Then, the one-parameter Lie group and invariant solutions of this considered equation are constructed. Subsequently, we applied a direct method to construct the optimal system of one-dimensional of this considered equation. Next, this considered higher-dimensional model can be reduced into the lower-dimensional fractional differential equations (FDEs) with the help of the three-parameter and two-parameter Erdélyi–Kober fractional differential operators (FDOs). Lastly, conservation laws of this discussed equation by using a new conservation theorem are also found. A series of results of the above obtained can provide strong support for us to reveal the mysterious veil of this viewed equation.