Abstract
A variable-coefficient Davey–Stewartson (vcDS) equation is investigated in this paper. Infinitesimal generators and symmetry groups are presented by the Lie group method, and the optimal system is presented with adjoint representation. Based on the optimal system, similarity reductions to partial differential equations (PDEs) are obtained, then some PDEs are reduced to ordinary differential equations (ODEs) by two-dimensional subalgebras, and the similarity solutions are provided, including periodic solutions and elliptic function solutions. With Lagrangian, it is shown that vcDS is nonlinearly self-adjoint. Furthermore, based on nonlinear self-adjointness, conservation laws for vcDS equation are derived.
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