Resonant Solutions to (3+1)-dimensional Bilinear Differential Equations

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

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

Abstract

In this thesis, we attempt to obtain a class of generalized bilinear differential equations in (3+1)-dimensions by D_p-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.

Scholar Commons Citation

Sun, Yue, "Resonant Solutions to (3+1)-dimensional Bilinear Differential Equations" (2016). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/6146