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An nth-order Darboux transformation for the one-dimensional time-dependent Schrödinger equation

- D. Arrigo, F. Hickling
- Mathematics
- 14 February 2003

Solutions for two one-dimensional Schr?dinger equations are linked together using an nth-order Darboux transformation. The resulting coefficients for these Darboux transformations give rise to a… Expand

On the determining equations for the nonclassical reductions of the heat and Burgers' equation

- D. Arrigo, F. Hickling
- Mathematics
- 15 June 2002

Abstract The determining equations for the nonclassical reductions of the heat and Burgers' equations are considered. It is shown that both systems belong to a Burgers' equation hierarchy. Each… Expand

Darboux transformations and linear parabolic partial differential equations

- D. Arrigo, F. Hickling
- Mathematics
- 19 July 2002

Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (n + 1) nonlinear partial differential equations. This… Expand

Darboux transformations and linear parabolic partial differential equations

- D. Arrigo, F. Hickling
- Mathematics
- Thirty-Sixth Southeastern Symposium on System…
- 27 September 2004

A method is provided to solve boundary value problems to parabolic partial differential equations of the form: u/sub t/ = u/sub x/x + f(x)u, provided f(x) is obtained as twice the second derivative… Expand

Darboux transformations for the reduced wave equation and its parabolic approximation

- D. Arrigo, F. Hickling
- Mathematics
- Thirty-Sixth Southeastern Symposium on System…
- 27 September 2004

The reduced wave equation with a variable wave speed and its parabolic approximation is considered. For each equation, a Darboux transformation is constructed. For the reduced wave equation, a… Expand

ON THE NATURAL DENSITY OF THE RANGE OF THE TERMINATING NINES FUNCTION

- R. K. Kennedy, Curtis N. Cooper, V. Drobot, F. Hickling
- Mathematics
- 1989

Noting that the expression (_n__) gives the number of terminating nines tl tO t which occur up to n but not including n, we will denote the above expression by t(n) and call t the "terminating nines… Expand

Critical Energy of Torus Knots

- F. Hickling, Wesley Davis, H. Woolverton
- Physics
- 1995

The energy of a smoothly parameterized knot y(t) is defined as rr \ i i lp7 \\dn dsdt Jo Jo \||7M-7(0f (D(t(s),T(t))) 2 j\\ds \\dt where D (y (s), y(t)) is the arc length between the two points y (s)… Expand