On Linear Superposition Principle Applying to Hirota Bilinear Equations

The linear superposition principle of exponential travelling waves is analysed for equations of Hirota bilinear type, with an aim to construct a specific subclass of N-soliton solutions formed by linear combination of exponential travelling waves. Applications are made for Sawada-Kotera and a (2+1)-dimensional equations, thereby presenting their N-wave solutions. An opposite question is also put forward and discussed about generating Hirota bilinear equations possesses the indicated N-wave solutions and a few illustrative examples are presented, together with an algorithm using weights.