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Darboux and binary Darboux transformations for discrete integrable systems I. Discrete potential KdV equation
- Source :
- Journal of Physics A: Mathematical and Theoretical. 47:025205
- Publication Year :
- 2013
- Publisher :
- IOP Publishing, 2013.
-
Abstract
- The Hirota–Miwa equation can be written in 'nonlinear' form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equation, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations.
- Subjects :
- Statistics and Probability
Pure mathematics
Integrable system
Wronskian
General Physics and Astronomy
Binary number
Statistical and Nonlinear Physics
Kadomtsev–Petviashvili equation
Connection (mathematics)
Nonlinear system
Nonlinear Sciences::Exactly Solvable and Integrable Systems
Modeling and Simulation
Korteweg–de Vries equation
Mathematical Physics
Mathematics
Gramian matrix
Subjects
Details
- ISSN :
- 17518121 and 17518113
- Volume :
- 47
- Database :
- OpenAIRE
- Journal :
- Journal of Physics A: Mathematical and Theoretical
- Accession number :
- edsair.doi...........8f4df66afe4bdb61dbd782ae56bcc2f2