2016/07/14 by Célestin Kurujyibwami, Kurujyibwami, Célestin, P. Basarab-Horwath +3
Engineering · Physics and Astronomy · #35A30 (Secondary) #35Q41 (Primary) 35B06 #Advanced Fiber Laser Technologies #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Photonic and Optical Devices #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1607.04118
openalex publication_date 2016/07/14 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We carry out the complete group classification of the class of\n(1+1)-dimensional linear Schr "odinger equations with complex-valued\npotentials. After introducing the notion of uniformly semi-normalized classes\nof differential equations, we compute the equivalence groupoid of the class\nunder study and show that it is uniformly semi-normalized. More specifically,\neach admissible transformation in the class is the composition of a linear\nsuperposition transformation of the corresponding initial equation and an\nequivalence transformation of this class. This allows us to apply the new\nversion of the algebraic method based on uniform semi-normalization and reduce\nthe group classification of the class under study to the classification of\nlow-dimensional appropriate subalgebras of the associated equivalence algebra.\nThe partition into classification cases involves two integers that characterize\nLie symmetry extensions and are invariant with respect to equivalence\ntransformations.\n