Linear superposition principle applying to Hirota bilinear equations
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 N -soliton solutions formed by linear combinations of exponential traveling waves. Applications are made for the 3+1 dimensional KP, JimboMiwa and BKP equations, thereby presenting their particular N N -wave solutions. An opposite question is also raised and discussed about generating Hirota bilinear equations possessing the indicated N N -wave solutions, and a few illustrative examples are presented, together with an algorithm using weights.
hirotas bilinear form soliton equations n n -wave solution n n n n n