THE LARGE‐TIME DEVELOPMENT OF THE SOLUTION TO AN INITIAL‐VALUE PROBLEM FOR THE KORTEWEG–DE VRIES EQUATION. II. INITIAL DATA HAS A DISCONTINUOUS COMPRESSIVE STEP

DOI10.1112/S0025579313000284zbMath1306.37086MaRDI QIDQ2874616

J. A. Leach, David John Needham

Publication date: 8 August 2014

Published in: Mathematika (Search for Journal in Brave)

zbMATH Keywords

Korteweg-de Vries equationlong-time asymptotic behaviordiscontinuous initial data

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Asymptotic expansions of solutions to PDEs (35C20) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (8)

Rarefaction waves of the Korteweg-de Vries equation via nonlinear steepest descent ⋮ Rarefaction waves for the Toda equation via nonlinear steepest descent ⋮ The large-time development of the solution to an initial-value problem for the Korteweg-de Vries equation: IV. Time dependent coefficients ⋮ Mini-workshop: Reflectionless operators: the Deift and Simon conjectures. Abstracts from the mini-workshop held October 22--28, 2017 ⋮ Whitham equations and phase shifts for the Korteweg–de Vries equation ⋮ The large-time development of the solution to an initial-value problem for the Korteweg-de Vries equation. III: Pure soliton solutions ⋮ The large-time development of the solution to an initial-boundary value problem for the Korteweg-de Vries equation on the negative quarter-plane ⋮ The focusing NLS equation with step-like oscillating background: the genus \(3\) sector

Cites Work

• The large-time development of the solution to an initial-boundary value problem for the Korteweg-de Vries equation. I: Steady state solutions
• The large-time development of the solution to an initial-boundary value problem for the Korteweg-de Vries equation on the negative quarter-plane
• A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation
• The large-time development of the solution to an initial-value problem for the Korteweg–de Vries equation: I. Initial data has a discontinuous expansive step
• A numerical and theoretical study of certain nonlinear wave phenomena
• Long-time asymptotics for the Korteweg–de Vries equation with step-like initial data
• Non-linear dispersive waves

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