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Analysis of Lie symmetries with conservation laws and solutions for the generalized (3 + 1)-dimensional time fractional Camassa-Holm-Kadomtsev-Petviashvili equation. (English) Zbl 1442.35517
Summary: 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.
MSC:
35R11 Fractional partial differential equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
Software:
HIROTA.MAX; MACSYMA
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References:
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