TY - JOUR
T1 - Rotational quotient procedure
T2 - A tracking control continuation method for PDEs on radially symmetric domains
AU - Kuo, Yueh Cheng
AU - Shieh, Shih Feng
AU - Wang, Weichung
N1 - Funding Information:
The authors are grateful to the anonymous referees for their comments and suggestions. This work is partially supported by the National Science Council , the National Center for Theoretical Sciences , and the Taida Institute of Mathematical Sciences in Taiwan .
PY - 2012/4
Y1 - 2012/4
N2 - Continuation methods are capable of finding multiform solutions by tracking solution curves. However, these methods may fail to track some desired solution curves due to the interference of the rotational equivalent solutions on a radially symmetric domain. We propose a rotational quotient procedure that applies extra constraints to standard continuation which overcomes this difficulty. We solve a time-independent nonlinear Schrödinger equation on a disk domain to demonstrate the functionality of the proposed method.
AB - Continuation methods are capable of finding multiform solutions by tracking solution curves. However, these methods may fail to track some desired solution curves due to the interference of the rotational equivalent solutions on a radially symmetric domain. We propose a rotational quotient procedure that applies extra constraints to standard continuation which overcomes this difficulty. We solve a time-independent nonlinear Schrödinger equation on a disk domain to demonstrate the functionality of the proposed method.
KW - Continuation methods
KW - Radially symmetric domain
KW - Rotation invariant solutions
UR - https://www.scopus.com/pages/publications/84862814791
UR - https://www.scopus.com/pages/publications/84862814791#tab=citedBy
U2 - 10.1016/j.cpc.2012.01.008
DO - 10.1016/j.cpc.2012.01.008
M3 - Article
AN - SCOPUS:84862814791
SN - 0010-4655
VL - 183
SP - 998
EP - 1001
JO - Computer Physics Communications
JF - Computer Physics Communications
IS - 4
ER -