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Group analysis and some solutions of a nonlinear wave equation. (English) Zbl 0717.73005

The authors study the invariance properties of the hyperbolic equation

(1)u tt -[f(u)u x +g(x,u)] x =0·

By imposing the invariance of the equation (1) with respect to an infinitesimal transformation group, some relations among f, g and the generators of the group are deduced. The result is then applied to some physical examples, in which it is also possible to describe exactly a family of invariant solutions to (1).

Reviewer: M.Degiovanni
MSC:
74E15Crystalline structure
74B20Nonlinear elasticity
35L70Nonlinear second-order hyperbolic equations
74H45Vibrations (dynamical problems in solid mechanics)
35L05Wave equation (hyperbolic PDE)
35A22Transform methods (PDE)