Newell-Whitehead-Segel equation,A Simpler Proof

Abstract

Previous analysis of the Newell-Whitehead-Segel equation proved the best solution is null; although, the method of solution generated complex nested integrals, therefore, difficult to analyze \cite{NWSgen,NWS2020}. Recent insights into the properties of the convolution integral enable considerable simplification of the solution in the codomain, producing much simpler representations. The inverse Fourier transform of the spectral solution proves to be a non-bijective, null solution, therefore, confirming previous suspicions. Alternative representations of the solution, either expansions or Fujita type solutions, all prove the solution to be a null function.