Analysis of Lie symmetries with conservation laws and solutions for the generalized [formula omitted]-dimensional time fractional Camassa–Holm–Kadomtsev–Petviashvili equation

Abstract

In this paper, under investigated is a generalized (3+1)-dimensional Camassa–Holm–Kadomtsev–Petviashvili (gCH-KP) equation, which describes the role of dispersion in the formation of patterns in liquid drops. With the help of the semi-inverse method, the Euler–Lagrange equation and Agrawal’s method, the time fractional gCH-KP equation is derived in the sense of Riemann–Liouville fractional derivatives. Further, the symmetry of the (3+1)-dimensional time fractional gCH-KP equation is studied by fractional order symmetry. Meanwhile, based on the new conservation theorem, the conservation laws of (3+1)-dimensional time fractional gCH-KP equation are constructed. Finally, the solutions to the equation are given via a bilinear method and the radial basis functions (RBFs) meshless approach.