In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods is developed for the nonlinear Schr\"odinger equation by combing the scalar auxiliary variable approach and the exponential Runge-Kutta method. By introducing an auxiliary variable, we first transform the original model into an equivalent system which admits both mass and modified energy  . Then applying the Lawson method and the symplectic Runge-Kutta method in time, we derive a class of mass- and energy-conserving time-discrete schemes  . Numerical experiments are addressed to demonstrate the accuracy and effectiveness of the newly proposed schemes.
In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods are developed for the nonlinear Schr\"odinger equation by combining the scalar auxiliary variable approach with the exponential Runge-Kutta method. By introducing an auxiliary variable, we first transform the original model into an equivalent system which admits both mass and modified energy conservation laws . Then applying the Lawson method and the symplectic Runge-Kutta method in time, we derive a class of mass- and energy-preserving time-discrete schemes which are arbitrarily high-order in time . Numerical experiments are addressed to demonstrate the accuracy and effectiveness of the newly proposed schemes.
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is
are
R
combing
combining
R
and
with
A
conservation laws
R
energy-conserving
energy-preserving
A
which are arbitrarily high-order in time