Functionals of the Peierls - Frölich type and variational principle for Whitham equations
نویسنده
چکیده
depending on the parameters x, t. We assume that the parameters are chosen in such a way that the function has unique minimum at the point u = u(x, t). This happens if t < 0 or 0 < t and |x| > 4t √ 2t. (2) Then the minimizer satisfies the equation of motion of one-dimensional ideal fluid (Riemann wave equation) ut = 6uux. (3) It solves the Cauchy problem for (3) with the initial data x = u for t = 0. (4)
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