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.
Ma and Fan REF showed that a linear superposition principle of exponential waves applied to Hirota bilinear equations, under some additional condition on the exponential waves and possibly on the polynomial as well.
Linear superposition principle applying to Hirota bilinear equations
Comput. Math. Appl.
Comput. Math. Appl.
Computer Science Mathematics