A complete group classification of a class of variable coefficient
(1+1)-dimensional telegraph equations f(x)utt​=(H(u)ux​)x​+K(u)ux​, is
given, by using a compatibility method and additional equivalence
transformations. A number of new interesting nonlinear invariant models which
have non-trivial invariance algebras are obtained. Furthermore, the possible
additional equivalence transformations between equations from the class under
consideration are investigated. Exact solutions of special forms of these
equations are also constructed via classical Lie method and generalized
conditional transformations. Local conservation laws with characteristics of
order 0 of the class under consideration are classified with respect to the
group of equivalence transformations.Comment: 23 page