Invariant analysis and exact solutions of nonlinear time fractional Sharma–Tasso–Olver equation by Lie group analysis

GW Wang, TZ Xu - Nonlinear Dynamics, 2014 - Springer
This paper is concerned with the time fractional Sharma–Tasso–Olver (FSTO) equation, Lie
point symmetries of the FSTO equation with the Riemann–Liouville derivatives are …

Lie symmetry analysis, optimal systems and exact solutions to the fifth-order KdV types of equations

H Liu, J Li, L Liu - Journal of Mathematical Analysis and Applications, 2010 - Elsevier
In this paper, the Lie symmetry analysis is performed on the fifth-order KdV types of
equations which arise in modeling many physical phenomena. The similarity reductions and …

Painlevé analysis, Lie symmetries and exact solutions for (2+ 1)-dimensional variable coefficients Broer–Kaup equations

S Kumar, K Singh, RK Gupta - Communications in Nonlinear Science and …, 2012 - Elsevier
A (2+ 1) dimensional Broer–Kaup system which is obtained from the constraints of the KP
equation is of importance in mathematical physics field. In this paper, the Painlevé analysis …

Exact solutions to Euler equation and Navier–Stokes equation

M Liu, X Li, Q Zhao - Zeitschrift für angewandte Mathematik und Physik, 2019 - Springer
The Lie symmetry analysis method and Bäcklund transformation method are proposed for
finding similarity reduction and exact solutions to Euler equation and Navier–Stokes …

New exact solutions for a generalized KdV equation

L Li, Y Xie, S Zhu - Nonlinear Dynamics, 2018 - Springer
In this paper, we establish a triple-order complete discrimination system to derive the
traveling wave solutions of the generalized KdV equation with high power nonlinearities …

Exact solutions and Painlevé analysis of a new (2+ 1)-dimensional generalized KdV equation

Y Zhang, Y Song, L Cheng, JY Ge, WW Wei - Nonlinear Dynamics, 2012 - Springer
Abstract The new (2+ 1)-dimensional generalized KdV equation which exists the bilinear
form is mainly discussed. We prove that the equation does not admit the Painlevé property …

Some invariant solutions of field equations with axial symmetry for empty space containing an electrostatic field

L Kaur, RK Gupta - Applied Mathematics and Computation, 2014 - Elsevier
The system of partial differential equations corresponding to a line element with axial
symmetry for empty space containing an electrostatic field has been examined. The …

Group classifications, optimal systems and exact solutions to the generalized Thomas equations

H Liu, J Li, L Liu, Y Wei - Journal of mathematical analysis and applications, 2011 - Elsevier
In this paper, the complete group classifications are performed on the types of Thomas
equations (TEs), which arise in the study of chemical exchange progress, etc., all of the …

Nonclassical symmetries and similarity solutions of variable coefficient coupled KdV system using compatibility method

RK Gupta, M Singh - Nonlinear Dynamics, 2017 - Springer
The variable coefficient KdV system is investigated for nonclassical symmetries using
compatibility method, and more general symmetries are reported. Several inequivalent …

Lie Symmetry analysis of the nonlinear Schrödinger equation with time dependent variable coefficients

P Devi, K Singh - International Journal of Applied and Computational …, 2021 - Springer
In this work, we study the generalized nonlinear Schrödinger equation having time
dependent variable coefficients by using Lie group method. We find the Lie point symmetries …