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Trilinear equations, Bell polynomials, and resonant solutions. (English) Zbl 1276.35131
Summary: A class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create trilinear differential equations. The resulting trilinear differential operators and equations are characterized by the Bell polynomials, and the superposition principle is applied to the construction of resonant solutions of exponential waves. Two illustrative examples are made by an algorithm using weights of dependent variables.

MSC:
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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