Search results for "Soliton resolution"

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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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