Linear superposition principle applying to Hirota bilinear equations

Abstract

A linear superposition principle of exponential traveling waves is analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N -soliton solutions formed by linear combinations of exponential traveling waves. Applications are made for the 3+1 dimensional KP, Jimbo–Miwa and BKP equations, thereby presenting their particular N -wave solutions. An opposite question is also raised and discussed about generating Hirota bilinear equations possessing the indicated N -wave solutions, and a few illustrative examples are presented, together with an algorithm using weights.