An energy-conserving Galerkin scheme for a class of nonlinear dispersive equations

A Galerkin scheme is presented for a class of conservative nonlinear dispersive equations, such as the Camassa-Holm equation and the regularized long wave equation. The scheme has two advantageous features: first, it is conservative in that it keeps the discrete analogue of the continuous energy conservation property in the original equations; second, it can be formulated only with cheap H^1-elements even if the original equations include third derivative u"x"x"x. Numerical experiments confirm the stability and effectiveness of the proposed scheme.

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