Construction of exact solutions in implicit form for PDEs: New functional separable solutions of non-linear reaction–diffusion equations with variable coefficients

摘要: Abstract The paper deals with different classes of non-linear reaction–diffusion equations variable coefficients c ( x ) u t = [ a f ] + b g , that admit exact solutions. direct method for constructing functional separable solutions to these and more complex mathematical physics is described. based on the representation in implicit form ∫ h d ξ ω η where functions are determined further by analyzing resulting functional-differential equations. Examples specific type their given. main attention paid fairly general form, which contain several arbitrary dependent unknown /or spatial (it important note PDEs, therefore have significant generality, great practical interest testing various numerical approximate analytical methods solving corresponding initial–boundary value problems). Many new generalized traveling-wave