## 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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### References:

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