The elliptic sine-Gordon equation - a nonlinear elliptic integrable PDE

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.
Original languageEnglish
Title of host publication Stock Image Unified Transform for Boundary Value Problems
Subtitle of host publicationApplications and Advances
EditorsA. S. Fockas, B. Pelloni
PublisherSIAM
Pages73-90
Number of pages18
ISBN (Print)9781611973815
Publication statusPublished - 2014

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Sine-Gordon Equation
Elliptic Equations
Lax Pair
Boundary Value Problem
Boundary conditions
Necessary Conditions
Formulation
Alternatives

Cite this

Pelloni, B. (2014). The elliptic sine-Gordon equation - a nonlinear elliptic integrable PDE. In A. S. Fockas, & B. Pelloni (Eds.), Stock Image Unified Transform for Boundary Value Problems: Applications and Advances (pp. 73-90). SIAM.
Pelloni, Beatrice. / The elliptic sine-Gordon equation - a nonlinear elliptic integrable PDE. Stock Image Unified Transform for Boundary Value Problems: Applications and Advances. editor / A. S. Fockas ; B. Pelloni. SIAM, 2014. pp. 73-90
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Pelloni, B 2014, The elliptic sine-Gordon equation - a nonlinear elliptic integrable PDE. in AS Fockas & B Pelloni (eds), Stock Image Unified Transform for Boundary Value Problems: Applications and Advances. SIAM, pp. 73-90.

The elliptic sine-Gordon equation - a nonlinear elliptic integrable PDE. / Pelloni, Beatrice.

Stock Image Unified Transform for Boundary Value Problems: Applications and Advances. ed. / A. S. Fockas; B. Pelloni. SIAM, 2014. p. 73-90.

Research output: Chapter in Book/Report/Conference proceedingChapter

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AB - In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.

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BT - Stock Image Unified Transform for Boundary Value Problems

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Pelloni B. The elliptic sine-Gordon equation - a nonlinear elliptic integrable PDE. In Fockas AS, Pelloni B, editors, Stock Image Unified Transform for Boundary Value Problems: Applications and Advances. SIAM. 2014. p. 73-90