Enhancing and essentially generalizing previous results on a class of (1+ 1)-dimensional
nonlinear wave and elliptic equations, we apply several new techniques to classify …

We carry out the extended symmetry analysis of an ultraparabolic Fokker–Planck equation
with three independent variables, which is also called the Kolmogorov equation and is …

We carry out the group classification of the class of two-dimensional shallow water
equations with variable bottom topography using an optimized version of the method of …

We discuss how point transformations can be used for the study of integrability, in particular,
for deriving classes of integrable variable-coefficient differential equations. The procedure of …

The complete group classification problem for the class of (1+ 1)-dimensional rth order
general variable-coefficient Burgers–Korteweg–de Vries equations is solved for arbitrary …

We classify the Lie symmetries of variable coefficient Gardner equations (called also the
combined KdV–mKdV equations). In contrast to the particular results presented in Molati and …

The group classification problem for the class of (1+ 1)-dimensional linear rth order evolution
equations is solved for arbitrary values of r> 2. It is shown that a related maximally gauged …

The equations describing the flow of a one-dimensional continuum in Lagrangian
coordinates are studied in this paper by the group analysis method. They are reduced to a …

We carry out the complete group classification of the class of (1+ 1)-dimensional linear
Schrödinger equations with complex-valued potentials. After introducing the notion of …

Abstract Within the class of (1+ 2)‐dimensional ultraparabolic linear equations, we
distinguish a fine Kolmogorov backward equation with a quadratic diffusivity. Modulo the …