
Dynamics of solutions in the generalized BenjaminOno equation: a numerical study
We consider the generalized BenjaminOno (gBO) equation on the real line...
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Higher dimensional generalization of the BenjaminOno equation: 2D case
We consider a higherdimensional version of the BenjaminOno (HBO) equat...
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On Linear Damping Around Inhomogeneous Stationary States of the VlasovHMF Model
We study the dynamics of perturbations around an inhomogeneous stationar...
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Numerical study of ZakharovKuznetsov equations in two dimensions
We present a detailed numerical study of solutions to the (generalized) ...
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Global bifurcation diagrams of positive solutions for a class of 1D superlinear indefinite problems
This paper analyzes the structure of the set of positive solutions of a ...
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Spatial and color hallucinations in a mathematical model of primary visual cortex
We study a simplified model of the representation of colors in the prima...
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A Reduced Order technique to study bifurcating phenomena: application to the GrossPitaevskii equation
We are interested in the steady state solution of the GrossPitaevskii e...
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Numerical study of soliton stability, resolution and interactions in the 3D ZakharovKuznetsov equation
We present a detailed numerical study of solutions to the ZakharovKuznetsov equation in three spatial dimensions. The equation is a threedimensional generalization of the Kortewegde Vries equation, though, not completely integrable. This equation is L^2subcritical, 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 <cit.> for a larger class of initial data. We then investigate the solution behavior for different localizations and rates of decay including exponential and algebraic decays, and give positive confirmation toward the soliton resolution conjecture in this equation. Finally, we investigate soliton interactions in various settings and show that there is both a quasielastic interaction and a strong interaction when two solitons merge into one, in all cases always emitting radiation in the conictype region of the negative xdirection.
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