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A complete group classification of a class of variable coefficient(1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, isgiven, by using a compatibility method and additional equivalencetransformations. A number of new interesting nonlinear invariant models whichhave non-trivial invariance algebras are obtained. Furthermore, the possibleadditional equivalence transformations between equations from the class underconsideration are investigated. Exact solutions of special forms of theseequations are also constructed via classical Lie method and generalizedconditional transformations. Local conservation laws with characteristics oforder 0 of the class under consideration are classified with respect to thegroup of equivalence transformations.Comment: 23 page

Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations