  In this paper, we present a quadratic auxiliary variable approach to develop
a new class of energy-preserving Runge-Kutta methods for the Korteweg-de Vries
equation. The quadratic auxiliary variable approach is first proposed to
reformulate the original model into an equivalent system, which transforms the
energy conservation law of the Korteweg-de Vries equation into two quadratic
invariants of the reformulated system. Then the symplectic Runge-Kutta methods
are directly employed for the reformulated model to arrive at a new kind of
time semi-discrete schemes for the original problem. Under the consistent
initial condition, the proposed methods are rigorously proved to maintain the
original energy conservation law of the Korteweg-de Vries equation. In
addition, the Fourier pseudo-spectral method is used for spatial
discretization, resulting in fully discrete energy-preserving schemes. To
implement the proposed methods effectively, we present a very efficient
iterative technique, which not only greatly saves the calculation cost, but
also achieves the purpose of practically preserving structure. Ample numerical
results are addressed to confirm the expected order of accuracy, conservative
property and efficiency of the proposed algorithms.
