Search results for "Soliton stability"

showing 2 items of 2 documents

Numerical study of soliton stability, resolution and interactions in the 3D Zakharov–Kuznetsov equation

2021

International audience; We present a detailed numerical study of solutions to the Zakharov-Kuznetsov equation in three spatial dimensions. The equation is a three-dimensional generalization of the Korteweg-de Vries equation, though, not completely integrable. This equation is L-2-subcritical, and thus, solutions exist globally, for example, in the H-1 energy space.We first study stability of solitons with various perturbations in sizes and symmetry, and show asymptotic stability and formation of radiation, confirming the asymptotic stability result in Farah et al. (0000) for a larger class of initial data. We then investigate the solution behavior for different localizations and rates of de…

Soliton stabilityIntegrable systemStrong interactionSoliton resolutionSpace (mathematics)01 natural sciencesStability (probability)Zakharov-Kuznetsov equationMathematics - Analysis of PDEsExponential stabilityFOS: MathematicsMathematics - Numerical Analysis0101 mathematics[MATH]Mathematics [math]Soliton interactionMathematical physicsPhysics[PHYS]Physics [physics]Radiation010102 general mathematicsStatistical and Nonlinear PhysicsNumerical Analysis (math.NA)Condensed Matter PhysicsSymmetry (physics)Exponential function010101 applied mathematicsNonlinear Sciences::Exactly Solvable and Integrable SystemsSolitonAnalysis of PDEs (math.AP)
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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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