Metamorphism -- an Integral Transform Reducing the Order of a Differential Equation

Abstract

We propose an integral transform, called metamorphism, which allow us to reduce the order of a differential equation. For example, the second order Helmholtz equation is transformed into a first order equation, which can be solved by the method of characteristics.

11 pages in AMS-LaTeX, 2 PDF images in one figure; v2: numerous minor improvements, v3: minor correction, a reference added

References in corpus (2)

• Solving the Schrodinger Equation by Reduction to a First-order Differential Operator through a Coherent States Transform
• Metamorphism as a covariant transform for the SSR group

Cited by in corpus (2)

• Cross-Toeplitz Operators on the Fock--Segal--Bargmann Spaces and Two-Sided Convolutions on the Heisenberg Group
• Metamorphism as a covariant transform for the SSR group