Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417546 | Journal of Mathematical Analysis and Applications | 2016 | 29 Pages |
â¢We extend the Darboux transformations on a space scale that contains Darboux transformations for discrete and continuous differential equations.â¢We extend Darboux's and Crum's theorems on a space scale.â¢We deduce the Korteweg-de Vries-like system of equations on a space scale.â¢We construct the solution of the system mentioned above by using the Darboux transformations.
Using the time/space-scale calculus introduced by Hilger, we describe a Darboux transformation for partial differential equations on a space scale, and extend the classical theorems of Darboux and Crum to this setting. As an application, we use the Lax equation to deduce a system of Korteweg-de Vries equations on a space scale, and obtain a solution to this system by using the Darboux transformation.