A　new　general　Jacobi　elliptic　function　rational　expansion　method,　which　is　more　general　and　powerful　than　the　tanh　method,　the　sine-cosine　method,　the　Jacobi　elliptic　function　method　and　the　extended　Jacobi　elliptic　function　method,　and　the　extended　Jacobi　elliptic　function　rational　expansion　method,　is　proposed　to　construct　abundant　rational　formal　exact　doubly　periodic　wave　solutions　of　systems　of　nonlinear　wave　equations.　When　the　modulus　m　→　1　or　0,　these　rational　formal　doubly　periodic　solutions　degenerate　as　solitary　wave　solutions　and　trigonometric　function　solutions.　And　the　method　can　be　automatically　carried　out　in　computer.　©　2012　IEEE.