Search results for "Singularity analysis"

showing 2 items of 2 documents

ON THE BOUSSINESQ HIERARCHY

2002

A new sequence of nonlinear evolution systems satisfying the zero curvature property is constructed, by using the invariant singularity analysis. All these systems are completely integrable and a pseudo-potential (linearization) is explicitly determined for each of them. The second system of the sequence is the Broer-Kaup system, which, as is well known, corresponds to the higher order Boussinesq approximation in describing shallow water waves.

Waves and shallow waterIntegrable systemLinearizationSingularity analysisMathematical analysisBoussinesq approximation (water waves)CurvatureNonlinear evolutionMathematicsWaves and Stability in Continuous Media
researchProduct

Non-preserved curvature conditions under constrained mean curvature flows

2014

We provide explicit examples which show that mean convexity (i.e. positivity of the mean curvature) and positivity of the scalar curvature are non-preserved curvature conditions for hypersurfaces of the Euclidean space evolving under either the volume- or the area preserving mean curvature flow. The relevance of our examples is that they disprove some statements of the previous literature, overshadow a widespread folklore conjecture about the behaviour of these flows and bring out the discouraging news that a traditional singularity analysis is not possible for constrained versions of the mean curvature flow.

Mathematics - Differential GeometryMean curvature flowMean curvatureConjectureEuclidean spaceSingularity analysis010102 general mathematicsMathematical analysisCurvature53C4401 natural sciencesConvexity010101 applied mathematicsMathematics - Analysis of PDEsDifferential Geometry (math.DG)Computational Theory and MathematicsFOS: MathematicsMathematics::Differential GeometryGeometry and Topology0101 mathematicsAnalysisAnalysis of PDEs (math.AP)Scalar curvatureMathematicsDifferential Geometry and its Applications
researchProduct