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Group classifications, symmetry reductions and exact solutions to the nonlinear elastic rod equations. (English) Zbl 1241.35198
Summary: A Lie symmetry analysis is performed on the three nonlinear elastic rod (NER) equations. The complete group classification of the generalized nonlinear elastic rod equations is obtained. The symmetry reductions and exact solutions to the equations are presented. Furthermore, by means of dynamical system and power series methods, the exact explicit solutions to the equations are investigated. It is shown that the combination of Lie symmetry analysis and dynamical system methods is a feasible approach to deal with symmetry reductions and exact solutions to nonlinear PDEs.
MSC:
35Q74PDEs in connection with mechanics of deformable solids
35B06Symmetries, invariants, etc. (PDE)
74K10Rods (beams, columns, shafts, arches, rings, etc.) in solid mechanics
35C07Traveling wave solutions of PDE
22E70Applications of Lie groups to physics; explicit representations
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