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