We apply the infinitesimal technique for calculating invariants for the family of nonlinear equations formulated in the title. We show that the infinite-dimensional equivalence Lie algebra has three functionally independent differential invariants of the second order. Knowledge of invariants of families of equations is essential for identifying distinctly different equations and therefore for the problem of group classification.
Full text: http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6X3D-48B5FXK-1&_user=6 44585&_coverDate=02%2F29%2F2004&_rdoc=1&_fmt=full&_orig=browse&_cdi=7296&_sort=d &_docanchor=&view=c&_ct=1&_acct=C000034638&_version=1&_urlVersion=0&_userid=6445 85&md5=985355b8ae8049576a5190ec3737bd51