Inverse scattering transform for the Degasperis-Procesi equation

Adrian Constantin; Rossen I. Ivanov; Jonatan Lenells

doi:10.1088/0951-7715/23/10/012

Inverse scattering transform for the Degasperis-Procesi equation

Adrian Constantin, Rossen I. Ivanov, Jonatan Lenells

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We develop the inverse scattering transform (IST) method for the Degasperis- Procesi equation. The spectral problem is an sl(3) Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST, such as the construction of fundamental analytic solutions, the formulation of a Riemann-Hilbert problem, and the implementation of the dressing method, are presented.

Original language	English
Pages (from-to)	2559-2575
Number of pages	17
Journal	Nonlinearity
Volume	23
Issue number	10
DOIs	https://doi.org/10.1088/0951-7715/23/10/012
Publication status	Published - Oct 2010

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title = "Inverse scattering transform for the Degasperis-Procesi equation",

abstract = "We develop the inverse scattering transform (IST) method for the Degasperis- Procesi equation. The spectral problem is an sl(3) Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST, such as the construction of fundamental analytic solutions, the formulation of a Riemann-Hilbert problem, and the implementation of the dressing method, are presented.",

author = "Adrian Constantin and Ivanov, \{Rossen I.\} and Jonatan Lenells",

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N2 - We develop the inverse scattering transform (IST) method for the Degasperis- Procesi equation. The spectral problem is an sl(3) Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST, such as the construction of fundamental analytic solutions, the formulation of a Riemann-Hilbert problem, and the implementation of the dressing method, are presented.

AB - We develop the inverse scattering transform (IST) method for the Degasperis- Procesi equation. The spectral problem is an sl(3) Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST, such as the construction of fundamental analytic solutions, the formulation of a Riemann-Hilbert problem, and the implementation of the dressing method, are presented.

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DO - 10.1088/0951-7715/23/10/012

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SN - 0951-7715

VL - 23

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EP - 2575

JO - Nonlinearity

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Inverse scattering transform for the Degasperis-Procesi equation

Abstract

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