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Zbl 1217.35164
Ma, Wen-Xiu; Fan, Engui
Linear superposition principle applying to Hirota bilinear equations. (English)
[J] Comput. Math. Appl. 61, No. 4, 950-959 (2011). ISSN 0898-1221

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 2000:: *35Q53 KdV-like equations
35C08
37K10 Completely integrable systems etc.

Keywords: Hirota's bilinear form; soliton equations; $N$-wave solution

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Zentralblatt MATH Berlin [Germany]