0000000000324105

AUTHOR

Anna Kazeykina

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Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation

2017

International audience; We study numerically the evolution of perturbed Korteweg-de Vries solitons and of well localized initial data by the Novikov-Veselov (NV) equation at different levels of the 'energy' parameter E. We show that as |E| -> infinity, NV behaves, as expected, similarly to its formal limit, the Kadomtsev-Petviashvili equation. However at intermediate regimes, i.e. when |E| is not very large, more varied scenarios are possible, in particular, blow-ups are observed. The mechanism of the blow-up is studied.

Soliton stability[ MATH ] Mathematics [math]media_common.quotation_subjectBlow-upInverse scatteringMathematics::Analysis of PDEsNonzero energyFOS: Physical sciencesGeneral Physics and Astronomy2-dimensional schrodinger operator01 natural sciencesStability (probability)Instability010305 fluids & plasmasMathematics - Analysis of PDEs[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesFOS: MathematicsLimit (mathematics)0101 mathematics[MATH]Mathematics [math]Nonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsLine (formation)Mathematicsmedia_commonMathematical physicsNovikov–Veselov equationNonlinear Sciences - Exactly Solvable and Integrable SystemsKadomtsev-petviashvili equationsApplied Mathematics010102 general mathematics[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]InstabilityStatistical and Nonlinear PhysicsMathematical Physics (math-ph)InfinityNonlinear Sciences::Exactly Solvable and Integrable SystemsWell-posednessNovikov Veselov equationInverse scattering problemExactly Solvable and Integrable Systems (nlin.SI)Energy (signal processing)Analysis of PDEs (math.AP)
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