CLC number:
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2019-03-19
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Yiu-yin Lee. Modified residue harmonic balance solution for coupled integrable dispersionless equations with disturbance terms[J]. Journal of Zhejiang University Science A, 2019, 20(4): 300-304.
@article{title="Modified residue harmonic balance solution for coupled integrable dispersionless equations with disturbance terms",
author="Yiu-yin Lee",
journal="Journal of Zhejiang University Science A",
volume="20",
number="4",
pages="300-304",
year="2019",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1900023"
}
%0 Journal Article
%T Modified residue harmonic balance solution for coupled integrable dispersionless equations with disturbance terms
%A Yiu-yin Lee
%J Journal of Zhejiang University SCIENCE A
%V 20
%N 4
%P 300-304
%@ 1673-565X
%D 2019
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1900023
TY - JOUR
T1 - Modified residue harmonic balance solution for coupled integrable dispersionless equations with disturbance terms
A1 - Yiu-yin Lee
J0 - Journal of Zhejiang University Science A
VL - 20
IS - 4
SP - 300
EP - 304
%@ 1673-565X
Y1 - 2019
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1900023
Abstract: This is a supplementary study of the solution method previously proposed by the author. The proposed method is used for solving three-coupled integrable dispersionless equations with disturbance terms. It has only been adopted for solving (1) a nonlinear beam problem, and (2) a nonlinear vibro-acoustic problem. In the solution process, the three-coupled nonlinear equations can be transformed into only one Duffing equation. The higher-level nonlinear solutions, which were ignored in the previous method, can be generated using the proposed approach. Hence, in each step in the solution, only one independent nonlinear algebraic equation need be solved. As in the previous method, the proposed method has the advantage that the periodic solutions are represented by Fourier functions rather than the tedious implicit functions. The solutions from the proposed method agree reasonably well with those obtained from the classical harmonic balance method.
This is a continuation of the author's study on the solutions of nonlinear coupled integrable dispersionless equations. The effect of disturbance terms is taken into consideration. Also, the proposed method can lead to higher-order nonlinear solution that is ignored in the old method.
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