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 symmetriesη(u)=uxx-H(u)ux2-A(u)ux-B(u)and first-order sign-invariants J(u)=ut-F(u)ux2-P(u)ux-T(u) on the solutions u(x,t)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.