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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.

35Q53KdV-like (Korteweg-de Vries) equations
35C08Soliton solutions of PDE
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
Full Text: DOI
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