Variational Method for Studying Solitons in the KdV equation
F. Cooper, C. Lucheroni, H. Shepard, P. Sodano
Abstract
We use a class of trial wave functions which are generalizations of gaussians to study single soliton approximate analytic solutions to the KdV equations. The variational parameters obey a Hamiltonian dynamics obtained from the Principle of Least Action. We get extremely accurate approximate single soliton solutions including their time dependence using this method.
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