Boussinesq Solitary-Wave as a Multiple-Time Solution of the Korteweg-de Vries Hierarchy

Abstract

We study the Boussinesq equation from the point of view of a multiple-time reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the Korteweg--de Vries hierarchy, we show that the solitary--wave of the Boussinesq equation is a solitary--wave satisfying simultaneously all equations of the Korteweg--de Vries hierarchy, each one in an appropriate slow time variable.

arXiv comment12 pages, RevTex (to appear in J. Math Phys.)

References in corpus (1)

• The Korteweg-de Vries Hierarchy and Long Water-Waves

Cited by in corpus (3)

• Integrable Theory of the Perturbation Equations
• The Bi-Hamiltonian Structure of the Perturbation Equations of KdV Hierarchy
• Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation