Method for Solving the Korteweg-deVries Equation

1967/11/06 by Clifford S. Gardner, J. M. Greene, Martin D. Kruskal +1 · 4,632 citations
Physics and Astronomy · Mathematics · #Cold Atom Physics and Bose-Einstein Condensates #Quantum, superfluid, helium dynamics #Nonlinear Photonic Systems #Korteweg–de Vries equation #Initial value problem #Physics #Constant (computer programming) #Mathematical physics #Mathematical analysis #Equation solving #Value (mathematics) #Applied mathematics #Mathematics #Partial differential equation #Quantum mechanics #Computer science #Nonlinear system

paper · doi:10.1103/physrevlett.19.1095

published in Physical Review Letters 19(19), 1095-1097 (American Physical Society)

openalex publication_date 1967/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A method for solving the initial-value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as |x|\ensuremath→\ensuremath∞. The method can be used to predict exactly the "solitons," or solitary waves, which emerge from arbitrary initial conditions. Solutions that describe any finite number of solitons in interaction can be expressed in closed form.

Citations

• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States

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