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An nth-order Darboux transformation for the one-dimensional time-dependent Schrödinger equation
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 aExpand
On the determining equations for the nonclassical reductions of the heat and Burgers' equation
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. EachExpand
Darboux transformations and linear parabolic partial differential equations
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. ThisExpand
Darboux transformations and linear parabolic partial differential equations
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 derivativeExpand
Darboux transformations for the reduced wave equation and its parabolic approximation
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, aExpand
ON THE NATURAL DENSITY OF THE RANGE OF THE TERMINATING NINES FUNCTION
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 ninesExpand
Critical Energy of Torus Knots
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