On Steady-State Multiple Resonances for a Modified Bretherton Equation-Reference-Cited by-同舟云学术

On Steady-State Multiple Resonances for a Modified Bretherton Equation

Published:2017-04-10 Issue:5 Volume:72 Page:487-491
ISSN:1865-7109
Container-title:Zeitschrift für Naturforschung A
language:en
Short-container-title:

Author:

Sun Jianglong¹²³,Cui Jifeng⁴,He Zihan⁵,Liu Zeng¹^ORCID

Affiliation:

1. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Hubei, China

2. Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics, Huazhong University of Science and Technology, Hubei, China

3. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai, China

4. College of Science, Inner Mongolia University of Technology, Inner Mongolia, China

5. College of Mechanical Engineering, Inner Mongolia University of Technology, Inner Mongolia, China

Abstract

Abstract In this article, a modified Bretherton equation is considered to further check if steady-state multiple resonances exist not only for water waves but also for other dispersive medium. The linear resonance condition analysis shows that different components may interact with each other so multiple resonances may happen. Convergent steady-state solutions are obtained by solution procedure based on the homotopy analysis method (HAM) and the collocation method. Amplitude spectrum analysis confirms that more components indeed join the resonance as the nonlinearity increases. This article suggests that steady-state multiple resonance may exist in other dispersive system.

Publisher

Walter de Gruyter GmbH

Subject

Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics

Link

https://www.degruyter.com/document/doi/10.1515/zna-2017-0047/pdf

Reference13 articles.

1. F. P. Bretherton, J. Fluid Mech. 20, 457 (1964).

2. P. A. Madsen and D. R. Fuhrman, J. Fluid Mech. 698, 304 (2012).

3. S. J. Liao, Proposed Homotopy Analysis Techniques for the Solution of Nonlinear Problem, PhD thesis, Shanghai Jiao Tong University (1992).

4. S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, CHAPMAN & HALL/CRC, Boca Raton 2003.

5. S. J. Liao, Homotopy Analysis Method in Nonlinear Differential Equations, Springer and Higher Education, Heidelberg 2012.

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