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RESEARCH PRODUCT

Numerical study of blow-up in solutions to generalized Kadomtsev-Petviashvili equations

Christian KleinRalf Peter

subject

Vries equationPhysicsApplied Mathematics010102 general mathematicsMathematical analysisMathematics::Analysis of PDEsNumerical Analysis (math.NA)Type (model theory)01 natural sciencesSupercritical fluid010101 applied mathematicsNonlinear systemSingularityNonlinear Sciences::Exactly Solvable and Integrable SystemsMathematics - Analysis of PDEsFOS: MathematicsDiscrete Mathematics and CombinatoricsMathematics - Numerical Analysis0101 mathematicsNonlinear Sciences::Pattern Formation and SolitonsAnalysis of PDEs (math.AP)

description

We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized initial data with a single minimum and single maximum. In the cases with blow-up, we use a dynamic rescaling to identify the type of the singularity. We present a discussion of the observed blow-up scenarios.

yearjournalcountryeditionlanguage
2013-10-19
http://arxiv.org/abs/1310.5215