Linear superposition principle applying to Hirota bilinear equations. (English) Zbl 1217.35164

Ma, Wen-Xiu; Fan, Engui

Comput. Math. Appl. 61, No. 4, 950-959 (2011).

Summary: 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.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35C08	Soliton solutions
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)

Keywords:

Hirota’s bilinear form; soliton equations; \(N\)-wave solution

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