Conserved quantities, continuation and compactly supported solutions of some shallow water models
Igor Leite Freire
Abstract
Abstract A proof that strong solutions of the Dullin–Gottwald–Holm equation vanishing on an open set of the (1 + 1) space-time are identically zero is presented. In order to do it, we use a geometrical approach based on the conserved quantities of the equation to prove a unique continuation result for its solutions. We show that this idea can be applied to a large class of equations of the Camassa–Holm type.
Topics & Concepts
ContinuationAnalytic continuationWaves and shallow waterMathematicsPure mathematicsMathematical analysisComputer scienceGeologyProgramming languageOceanographyNonlinear Waves and SolitonsAdvanced Mathematical Physics ProblemsOcean Waves and Remote Sensing