Linear Subspaces of Solutions Applied to Hirota Bilinear Equation

Linear subspace of solution is applied to Boussinesq and Kadomtseve-Petviashvili (KP) equations using Hirota bilinear transformation. A sufficient and necessary condition for the existence of linear subspaces of exponential travelling wave solutions to Hirota bilinear equations is applied to show that multivariate polynomials whose zeros form a vector space can generate the desire Hirota bilinear equations with given linear subspaces of solutions and formulate such multivariate polynomials by using multivariate polynomials which have one and only one zero