Exact solutions and generalized conditional symmetries to (1 + 1)-dimensional reaction-diffusion equations

For the (1 + 1)-dimensional nonlinear reaction-diffusion equations, we obtain conditions under which the equations admit a class of second-order generalized conditional symmetries ) = u xx - H ( u ) u x 2 - A ( u ) u x - B ( u ) rst-order sign-invariants J ( u ) = u t - F ( u ) u x 2 - P ( u ) u x - T ( u ) on the solutions u ( x , t ) . Several different generalized conditional symmetries and first-order sign-invariants for equations are presented. Exact solutions to the resulting equations corresponding to the generalized conditional symmetries and first-order sign-invariants are constructed.