Numerical simulation of a solitonic gas in KdV and KdV–BBM equations
Copyright policy )Numerical simulation of a solitonic gas in KdV and KdV–BBM equations
The collective behaviour of soliton ensembles (i.e. the solitonic gas) 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.
19 pages, 11 figures, 47 references. Other author's papers can be found at http://www.denys-dutykh.com/
- Nizhny Novgorod State Pedagogical University Russian Federation
- French National Centre for Scientific Research France
- Laboratoire de Mathématiques France
- National Research University Higher School of Economics Russian Federation
- Institute of Applied Physics Russian Federation
[PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], KdV equation, [PHYS.PHYS.PHYS-CLASS-PH]Physics [physics]/Physics [physics]/Classical Physics [physics.class-ph], FOS: Physical sciences, Gas dynamics (general theory), Physics - Classical Physics, Pattern Formation and Solitons (nlin.PS), 530, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], 510, Stokes--Ursell number, [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], 76B25, [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Statistics and Probability [physics.data-an], [PHYS.PHYS.PHYS-AO-PH]Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph], statistical moments, [PHYS.PHYS.PHYS-DATA-AN]Physics [physics]/Physics [physics]/Data Analysis, Classical Physics (physics.class-ph), BBM equation, Nonlinear Sciences - Pattern Formation and Solitons, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], 76B15, 35Q53, KdV equations (Korteweg-de Vries equations), statistical description, Stokes-Ursell number, Numerical methods of time-dependent statistical mechanics, solitonic gas, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
[PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], KdV equation, [PHYS.PHYS.PHYS-CLASS-PH]Physics [physics]/Physics [physics]/Classical Physics [physics.class-ph], FOS: Physical sciences, Gas dynamics (general theory), Physics - Classical Physics, Pattern Formation and Solitons (nlin.PS), 530, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], 510, Stokes--Ursell number, [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], 76B25, [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Statistics and Probability [physics.data-an], [PHYS.PHYS.PHYS-AO-PH]Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph], statistical moments, [PHYS.PHYS.PHYS-DATA-AN]Physics [physics]/Physics [physics]/Data Analysis, Classical Physics (physics.class-ph), BBM equation, Nonlinear Sciences - Pattern Formation and Solitons, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], 76B15, 35Q53, KdV equations (Korteweg-de Vries equations), statistical description, Stokes-Ursell number, Numerical methods of time-dependent statistical mechanics, solitonic gas, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
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