Journal of Nonlinear Mathematical Physics

Novikov superalgebras are related to the quadratic conformal superalgebras which correspond to the Hamiltonian pairs and play fundamental role in the completely integrable systems. In this note, we divide Novikov superalgebras into two types: N and S. Then we show that the Novikov superalgebras of dimension...

The article deals with local symmetries of the infinite-order jet space of C∞-smooth curves in ℝm+1 (m ≥ 1). Transformations under consideration are the most general possible: they need not preserve the distinction between dependent and independent variables and the order of derivatives may be arbitrarily...

Invariant linearization criteria for square systems of second-order quadratically nonlinear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in the first derivatives. It is shown that there are two branches...

The conserved quantities for the heated radial liquid jet and the heated radial free jet are established by using conservation laws. The flow in a heated radial jet is described by Prandtl's momentum boundary layer equation, the continuity equation and the energy equation. Viscous dissipation is...

We indicate how one can extend any dynamical system (namely, any system of nonlinearly coupled autonomous ordinary differential equations) so that the extended dynamical system thereby obtained is either isochronous or asymptotically isochronous or multi-periodic, namely its generic solutions are either...

We consider Lotka–Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding...

This paper introduces a new type of symmetry reductions called extended nonclassical symmetries that can be studied for parameter identification problems described by partial differential equations. Including the data function in the parameter space, we show that specific data and parameter classes that...