  This paper is devoted to multi-parameter eigenvalue problems for perturbed
$p$-Laplacians, modelling travelling waves for a class of non-linear evolution
PDE. Dispersion relations between the eigen-para-meters, the existence of
eigenvectors and positive eigenvectors, variational principles for eigenvalues
of perturbed $p$-Laplacians and constructing analytical solutions are the main
subject of this paper. Besides the $p$-Laplacian-like eigenvalue problems we
also deal with new and non-standard eigenvalue problems, which can not be
solved by the methods used in nonlinear eigenvalue problems for $p$-Laplacians
and similar operators. We do both: extend and use classical variational and
analytical techniques to solve standard eigenvalue problems and suggest new
variational and analytical methods to solve the non-standard eigenvalue
problems we encounter in the search for travelling waves.
