Yet that weakness is also its greatest strength. People like the model because they can
easily understand its assumptions. The model is often good as a? rst approximation, and if …

A necessary and sufficient condition is established for the existence of a 1-1 transformation
of a system of nonlinear differential equations to a system of linear equations. The obtained …

We carry out an extensive investigation of conservation laws and potential symmetries for
the class of linear (1+ 1)-dimensional second-order parabolic equations. The group …

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 …

Simple and systematic algorithms for relating differential equations are given. They are
based on comparing the local symmetries admitted by the equations. Comparisons of the …

Bäcklund transformations (BTs) are considered for nonlinear parabolic equations of the form
ut+ uxx+ H (ux, u, x, t)= 0.(*) The most general form of both the BT and the class (*) is …

A constructive algorithm is developed to determine whether or not a given linear pde can be
mapped into a linear pde with constant coefficients. The algorithm is based on analyzing the …

We propose an approach to compute the boundary crossing probabilities for a class of
diffusion processes which can be expressed as piecewise monotone (not necessarily one-to …

In this paper, we study the classical problem of the first hitting time density to a moving
boundary for a diffusion process, which satisfies the Cherkasov condition, and hence, can …

Semi-invariants for the linear parabolic equations with two independent variables (time
variable t and space variable x) and one dependent variable u are derived under the …