Author

Yue Sun

Graduation Year

2016

Document Type

Thesis

Degree

M.A.

Degree Name

Master of Arts (M.A.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Wen-Xiu Ma, Ph.D.

Committee Member

Thomas J. Bieske, Ph.D.

Committee Member

Jing Yu, Ph.D.

Committee Member

Shouting Chen, Ph.D.

Keywords

Dp-operators, Hirota's bilinear method, Linear superposition principle, Resonance of solitons, Solitons

Abstract

In this thesis, we attempt to obtain a class of generalized bilinear differential equations in (3+1)-dimensions by Dp-operators with p=5, which have resonant solutions. We construct resonant solutions by using the linear superposition principle and parameterizations of wave numbers and frequencies. We test different values of p in Maple computations, and generate three classes of generalized bilinear differential equations and their resonant solutions when p=5.

Included in

Mathematics Commons

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