The Davey-Stewartson I Equation on the Quarter Plane with Homogeneous Dirichlet Boundary Conditions

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dc.creatorFokas, A. S.
dc.date2004-12-01
dc.date.accessioned2026-07-07T05:36:07Z
dc.date.available2026-07-07T05:36:07Z
dc.descriptionDromions are exponentially localised coherent structures supported by nonlinear integrable evolution equations in two spatial dimensions.In the study of initial-value problems on the plane, such solutions occur only if one imposes nontrivial boundary conditions at infinity, a situation of dubious physical significance. However it is established here that dromions appear naturally in the study of boundary-value problems. In particular, it is shown that the long time asymptotics of the solution of the Davey-Stewartson I equation in the quarter plane with arbitrary initial conditions and with zero Dirichlet boundary conditions is dominated by dromions. The case of non-zero Dirichlet boundary conditions is also discussed.
dc.identifierhttps://arxiv.org/abs/nlin/0412005
dc.identifierhttp://arxiv.org/abs/nlin/0412005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80885
dc.subjectExactly Solvable and Integrable Systems
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.titleThe Davey-Stewartson I Equation on the Quarter Plane with Homogeneous Dirichlet Boundary Conditions
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