摘要
Lie symmetry group method is applied to study the transonic pressure-gradient equations in two-dimensionalspace.Its symmetry groups and corresponding optimal systems are determined,and several classes of irrotational groupinvariantsolutions associated to the symmetries are obtained and special case of one-dimensional rarefaction wave isfound.
基金
Supported by the National Natural Science Foundation of China under Grant Nos. 11071195 and 10926082
China Postdoctoral Science Foundation under Grant No. 20090461305
the National Natural Science Foundation of Shaanxi Province under Grant No. 2009JQ1003
the Program of Shmunxi Provincial Department of Education under Grant Nos. 09JK770 and 11JK0482
