VARIATIONAL METHOD FOR STUDYING SOLITONS IN THE KORTEWEG-DEVRIES EQUATION

We use a variation method based on the principle of least action to obtain approximate time-dependent single soliton solutions to the KdV equation. A class of trial variational functions of the form u (x, t) = -A (t) exp [-beta(t) \x- q(t)\2n], with n a continuous real variable, is used to parametrize time-dependent solutions. We find that this class of trial functions leads to soliton-like solutions for all n, moving with fixed shape and constant velocity, and with energy and mass conserved. Minimizing the energy of the soliton with respect to the parameter n, we obtain a variational solution that gives an extremely accurate approximation to the exact solution.