6533b851fe1ef96bd12a8fd8

RESEARCH PRODUCT

A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions

Christian KleinTamara Grava

subject

Nonlinear Sciences - Exactly Solvable and Integrable SystemsNumerical analysis010102 general mathematicsMathematical analysisMathematics::Analysis of PDEsFOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Condensed Matter Physics01 natural sciences010101 applied mathematicsMathematics - Analysis of PDEsNonlinear Sciences::Exactly Solvable and Integrable SystemsFOS: MathematicsLimit (mathematics)Exactly Solvable and Integrable Systems (nlin.SI)0101 mathematicsDispersion (water waves)Korteweg–de Vries equationSettore MAT/07 - Fisica MatematicaNonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsAnalysis of PDEs (math.AP)MathematicsMathematical physics

description

Abstract We study numerically the small dispersion limit for the Korteweg–de Vries (KdV) equation u t + 6 u u x + ϵ 2 u x x x = 0 for ϵ ≪ 1 and give a quantitative comparison of the numerical solution with various asymptotic formulae for small ϵ in the whole ( x , t ) -plane. The matching of the asymptotic solutions is studied numerically.

yearjournalcountryeditionlanguage
2012-02-05Phys. D 241 (2012), no. 23-24, 2246–2264
10.1016/j.physd.2012.04.001http://dx.doi.org/10.1016/j.physd.2012.04.001