A property of the defining equations for the Lie algebra in the group classification problem for wave equations.
Applications of group analysis to the three-dimensional equations of fluids with internal inertia.
Consequences of symmetries on the analysis and construction of turbulence models.
Exact solution of the time fractional variant Boussinesq-Burgers equations
In the present article, we consider a nonlinear time fractional system of variant Boussinesq-Burgers equations. Using Lie group analysis, we derive the infinitesimal groups of transformations containing some arbitrary constants. Next, we obtain the system of optimal algebras for the symmetry group of transformations. Afterward, we consider one of the optimal algebras and construct similarity variables, which reduces the given system of fractional partial differential equations (FPDEs) to fractional...
Group-theoretical solutions to gas dynamic equations generated by three-dimensional Lie subalgebras.
Invariant tensors and partial differential equations.
Irregular partially invariant solutions of rank 2 and defect 1 to equations of gas dynamics.
Lie group analysis of a flow with contaminant-modified viscosity.
On power series solutions for the Euler equation, and the Behr–Nečas–Wu initial datum
We consider the Euler equation for an incompressible fluid on a three dimensional torus, and the construction of its solution as a power series in time. We point out some general facts on this subject, from convergence issues for the power series to the role of symmetries of the initial datum. We then turn the attention to a paper by Behr, Nečas and Wu, ESAIM: M2AN 35 (2001) 229–238; here, the authors chose a very simple Fourier polynomial as an initial datum for the Euler equation and analyzed...
Solutions of shallow-water equations in non-rectangular cross-section channels.
Solvability of the initial boundary-value problems for hyperbolic model of ideal incompressible liquid motion.
Symmetries and solutions to equations of two-dimensional motions of polytropic gas.
Symmetry group analysis and invariant solutions of hydrodynamic-type systems.
The effects of nonuniform surface tension on the axisymmetric gravity-driven spreading of a thin liquid drop.
The two-dimensional eikonal equation.
Time fractional Kupershmidt equation: symmetry analysis and explicit series solution with convergence analysis
In this work, the fractional Lie symmetry method is applied for symmetry analysis of time fractional Kupershmidt equation. Using the Lie symmetry method, the symmetry generators for time fractional Kupershmidt equation are obtained with Riemann-Liouville fractional derivative. With the help of symmetry generators, the fractional partial differential equation is reduced into the fractional ordinary differential equation using Erdélyi-Kober fractional differential operator. The conservation laws are...