Complete group classifications and symmetry reductions of the fractional fifth‐order KdV types of equations

H Liu - Studies in Applied Mathematics, 2013 - Wiley Online Library
This paper is concerned with the fractional fifth‐order KdV types of equations, the complete
group classification is performed on the general fractional fifth‐order partial differential …

Codimension two Lie invariant solutions of the modified Khokhlov–Zabolotskaya–Kuznetsov equation

P Satapathy, T Raja Sekhar… - Mathematical Methods in …, 2021 - Wiley Online Library
Invariant solutions for the modified Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation are
obtained by using classical Lie symmetries. The complete set of local point symmetries is …

Study of wave propagation in arterial blood flow under symmetry analysis

S Shagolshem, B Bira, D Zeidan - Mathematical Methods in the …, 2023 - Wiley Online Library
In this paper, we address a one‐dimensional quasi‐linear hyperbolic system of equations
describing blood flow through compliant axi‐symmetric vessels. From the symmetry …

Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid

H Liu, Y Geng - Journal of Differential Equations, 2013 - Elsevier
In this paper, the systems of carbon nanotubes (CNTs) conveying fluid are considered by the
combination of Lie symmetry analysis and the dynamical system method. All of the …

[HTML][HTML] Symmetry reductions, dynamical behavior and exact explicit solutions to the Gordon types of equations

H Liu, J Li - Journal of Computational and Applied Mathematics, 2014 - Elsevier
In this paper, the combination of Lie symmetry analysis and the dynamical system method is
performed on the mixed second-order sine-Gordon equation, all of the geometric vector …

Lie symmetries, integrable properties and exact solutions to the variable-coefficient nonlinear evolution equations

H Liu, C Yue - Nonlinear Dynamics, 2017 - Springer
This paper is concerned with the variable-coefficient nonlinear evolution equations, which
include the cylindrical KdV types of equations. By the combination of Painlevé analysis and …

[HTML][HTML] Nonlocal symmetries, exact solutions and conservation laws of the coupled Hirota equations

X Xin, Y Liu, X Liu - Applied Mathematics Letters, 2016 - Elsevier
Using the Lax pair, nonlocal symmetries of the coupled Hirota equations are obtained. By
introducing an appropriate auxiliary dependent variable, the nonlocal symmetries are …

RETRACTED: Lie symmetry analysis, optimal system and exact solutions for variable-coefficients (2+ 1)-dimensional dissipative long-wave system

X Yan, J Liu, J Yang, X Xin - 2023 - Elsevier
Errors in the mathematical derivations have been identified that are found to be unfixable.
Such errors have rendered the main results in the paper erroneous. The authors apologise …

Group classification, symmetry reductions and exact solutions of the time-fractional generalized thin film equation with variable coefficients

Q Gu, L Wang - Computational and Applied Mathematics, 2023 - Springer
In this paper, we investigate the time-fractional generalized thin film equation (TFGTFE) with
two arbitrary functions and perform the group classification with respect to these arbitrary …

Group classifications, optimal systems, symmetry reductions and conservation law of the generalized fractional porous medium equation

Q Gu, L Wang, Y Yang - … in Nonlinear Science and Numerical Simulation, 2022 - Elsevier
This paper investigates the generalized fractional porous medium equations (GFPMEs)
which are the generalizations of the dual porous medium equation with integer order …