Title :
Darboux transformations for the reduced wave equation and its parabolic approximation
Author :
Arrigo, Daniel J. ; Hickling, Fred
Author_Institution :
Dept. of Mathematics, Central Arkansas Univ., Conway, AR, USA
Abstract :
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 Darboux transformation is obtained linking solutions to Laplace´s equation. For the parabolic approximation equation, a transformation is obtained linking solutions to Schrodinger´s equation. It is shown that these transformations exist for the same class of variable wave speed.
Keywords :
Laplace transforms; Schrodinger equation; nonlinear systems; parabolic equations; Darboux transformations; Laplace equation; Schrodinger equation; nonlinear system; parabolic approximation equation; reduced wave equation; Differential equations; Joining processes; Laplace equations; Mathematics; Partial differential equations; Schrodinger equation; Transforms;
Conference_Titel :
System Theory, 2004. Proceedings of the Thirty-Sixth Southeastern Symposium on
Print_ISBN :
0-7803-8281-1
DOI :
10.1109/SSST.2004.1295677
