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

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

1995-07-31

arxiv.org/abs/patt-sol/9507005v2

Nonlinear Sciences

Pattern Formation and Solitons

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

Scientific paper

10.1063/1.531190

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.

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