摘要
The paper proposes a family of novel arbitrary high-order structurepreserving exponential schemes for the nonlinear Schrodinger equation.First,we introduce a quadratic auxiliary variable to reformulate the original nonlinear Schrodinger equation into an equivalent equation with modified energy.With that,the Lawson transformation technique is applied to the equation and deduces a conservative exponential system.Then,the symplectic Runge-Kutta method approximates the exponential system in the time direction and leads to a semi-discrete conservative scheme.Subsequently,the Fourier pseudo-spectral method is applied to approximate the space of the semi-discrete to obtain a class of fully-discrete schemes.The constructed schemes are proved to inherit quadratic invariants and are stable.Some numerical examples are given to confirm the accuracy and conservation of the developed schemes at last.
基金
supported by the National Natural Science Foundation of China(Grant Nos.11971412 and 12001471)
the Scientific research Fund of Hunan Provincial Education Department(No.20A484)
the Natural Science Foundation of Henan Province(No.222300420280)
the Natural Science Foundation of Hunan Province(No.2023JJ40656)
the scientific research Fund of Xuchang University(No.2024ZD010).
