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Author Dutykh, Denys ♦ Pelinovsky, Efim
Source CiteSeerX
Content type Text
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Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Non-integrable Model ♦ Numerical Simulation ♦ Solitonic Gas Integrable ♦ Nonlinear Effect ♦ Stokes Ursell Number ♦ Asymptotic Method ♦ High Resolution Numerical Result ♦ Celebrated Kdv Equation ♦ Integrable Model ♦ Bbm Term ♦ Important Statistical Characteristic ♦ Monte Carlo Simulation ♦ Solitonic Gas ♦ Relative Importance ♦ Statistical Description ♦ Direct Numerical Simulation ♦ Non-integrable Kdv Bbm Type Model ♦ Nonintegrable Case ♦ Bbm Equation ♦ Key Word ♦ Kdv Equation ♦ Free Surface Elevation Probability Distribution
Abstract Abstract. Thecollectivebehaviourofsolitonensembles(i.e. the solitonicgas)is studied using the methods of the direct numerical simulation. Traditionally this problem was addressed in the context of integrable models such as the celebrated KdV equation. We extend this analysis to non-integrable KdV–BBM type models. Some high resolution numerical results are presented in both integrable and nonintegrable cases. Moreover, the free surface elevation probability distribution is shown to be quasi-stationary. Finally, we employ the asymptotic methods along with the Monte–Carlo simulations in order to study quantitatively the dependence of some important statistical characteristics (such as the kurtosis and skewness) on the Stokes–Ursell number (which measures the relative importance of nonlinear effects compared to the dispersion) and also on the magnitude of the BBM term. Key words and phrases: solitonic gas; KdV equation; BBM equation; statistical description;
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 2013-01-01