RESEARCH RTICLE

Trilinear equations, Bell polynomials, and resonant solutions

  • Wen-Xiu MA
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  • Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA

Received date: 11 Feb 2013

Accepted date: 18 Jun 2013

Published date: 01 Oct 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

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.

Cite this article

Wen-Xiu MA . Trilinear equations, Bell polynomials, and resonant solutions[J]. Frontiers of Mathematics in China, 2013 , 8(5) : 1139 -1156 . DOI: 10.1007/s11464-013-0319-5

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