TY - JOUR
T1 - Novel High-Order Mass- and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrödinger Equation 
AU - Qian , Xu
AU - Zhang , Hong
AU - Yan , Jingye
AU - Song , Songhe
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 993
EP - 1012
PY - 2023
DA - 2023/11
SN - 16
DO - http://doi.org/10.4208/nmtma.OA-2022-0185
UR - https://global-sci.org/intro/article_detail/nmtma/22120.html
KW - Regularized logarithmic Schrödinger equation, conservative numerical integrators, invariant energy quadratization approach, diagonally implicit Runge-Kutta scheme.
AB - <p style="text-align: justify;">We develop a class of conservative integrators for the regularized logarithmic Schrödinger equation (RLogSE) using the quadratization technique and
symplectic Runge-Kutta schemes. To preserve the highly nonlinear energy functional, the regularized equation is first transformed into an equivalent system that
admits two quadratic invariants by adopting the invariant energy quadratization
approach. The reformulation is then discretized using the Fourier pseudo-spectral
method in the space direction, and integrated in the time direction by a class of
diagonally implicit Runge-Kutta schemes that conserve both quadratic invariants to
round-off errors. For comparison purposes, a class of multi-symplectic integrators
are developed for RLogSE to conserve the multi-symplectic conservation law and
global mass conservation law in the discrete level. Numerical experiments illustrate
the convergence, efficiency, and conservative properties of the proposed methods.</p>