On the realization of nonlinear wave profiles using the Banach fixed- point theorem: Stokes wave in a finite depth

Taek S. Jang; S.H. Kwon; Takeshi Kinoshita

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On the realization of nonlinear wave profiles using the Banach fixed- point theorem: Stokes wave in a finite depth

机译：使用Banach不动点定理实现非线性波剖面的研究：有限深度的斯托克斯波

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A new mathematical formulation for the realization of nonlinear wave profiles and its nonlinear solution procedure, based on the Banach fixed-point theorem, is proposed. To apply the formulation, a nonlinear equation for the Stokes wave in a finite depth was derived, and some numerical solutions are given. A numerical study showed that the proposed iteration method, based on linear progressive wave potential only, enabled us to realize the Stokes nonlinear wave profiles in a finite depth. The nonlinear strategy of iteration has a very fast convergence rate, i.e., only about 6-10 iterations are required to obtain a numerically converged solution.

机译：提出了一种基于Banach不动点定理的非线性波谱实现及其非线性求解过程的新数学公式。为了应用该公式，推导了有限深度内斯托克斯波的非线性方程，并给出了一些数值解。数值研究表明，所提出的仅基于线性渐进波势的迭代方法使我们能够在有限的深度上实现斯托克斯非线性波轮廓。迭代的非线性策略具有非常快的收敛速度，即，仅需要大约6-10次迭代即可获得数值收敛解。

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《Journal of marine science and technology》 |2005年第4期|p.181-187|共7页
作者
Taek S. Jang; S.H. Kwon; Takeshi Kinoshita;
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作者单位

Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan 609-735, Korea;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类水路运输;
关键词
banach fixed-point theorem; stokes wave in a finite depth; fast convergence rate;

机译：banach定点定理;有限深度的焦波;快速收敛;

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1. Nonlinear wave profiles of wave-wave interaction in a finite water depth by fixed point approach [J] . T.S. Jang, S.H. Kwon, H.S. Choi Ocean Engineering . 2007,第3a4期

机译：固定点法在有限水深处波波相互作用的非线性波剖面
2. The Fourth-Order Nonlinear Schrodinger Equation for the Envelope of Stokes Waves on the Surface of a Finite-Depth Fluid [J] . Yu. V. Sedletsky Journal of Experimental and Theoretical Physics . 2003,第1期

机译：有限深度流体表面上斯托克斯波包络的四阶非线性薛定inger方程
3. Nonlinear Wave Interaction of Three Stokes' Waves in Deep Water: Banach Fixed Point Method [J] . Taek S. Jang, S. H. Kwon, Beom J. Kim Journal of Mechanical Science and Technology . 2006,第11期

机译：深水中三个斯托克斯波的非线性波相互作用：Banach不动点法
4. A UNIFIED COUPLED-MODE APPROACH TO NONLINEAR WAVES IN FINITE DEPTH. POTENTIAL FLOW [C] . G.A. Athanassoulis, K. A. Belibassakis 27th international conference on offshore mechanics and arctic engineering 2008 . 2008

机译：有限深度非线性波的统一耦合模式方法。潜在流量
5. Nonlinear analysis of waves in finite water depth. [D] . Ahn, Kyungmo. 1993

机译：有限水深中波浪的非线性分析。
6. Strong convergence theorems for a common zero of a finite family of H-accretive operators in Banach space [O] . Huimin He, Sanyang Liu, Rudong Chen -1

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7. The effect of third-order nonlinearity on statistical properties of random directional waves in finite depth [O] . A. Toffoli, M. Benoit, M. Onorato, 2009

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8. Dense Sets and the Projection Theorem for Acoustic Harmonic Waves in a Homogeneous Finite Depth Ocean [R] . Gilbert, R. P. , Xu, Y. 1988

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On the realization of nonlinear wave profiles using the Banach fixed- point theorem: Stokes wave in a finite depth

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