scholarly journals An iterative method to compute conformal mappings and their inverses in the context of water waves over topographies

2021 ◽  
Author(s):  
M. V. Flamarion ◽  
R. Ribeiro
Keyword(s):  
Iterative Method ◽  
Water Waves ◽  
Conformal Mappings

Water waves over a variable bottom: a non-local formulation and conformal mappings

2012 ◽  
Vol 695 ◽  
pp. 288-309 ◽  
Author(s):  
A. S. Fokas ◽  
A. Nachbin
Keyword(s):  
Water Waves ◽  
Conformal Mappings ◽  
The Novel ◽  
Local Equation ◽  
Flat Bottom ◽  
Weakly Nonlinear ◽  
Variable Bottom ◽  
Non Local ◽  
Three Space ◽  
Non Local Equations

AbstractIn Ablowitz, Fokas & Musslimani (J. Fluid Mech., vol. 562, 2006, pp. 313–343) a novel formulation was proposed for water waves in three space dimensions. In the flat-bottom case, this formulation consists of the Bernoulli equation, as well as of a non-local equation. The variable-bottom case, which now involves two non-local equations, was outlined but not explored in the above paper. Here, the variable-bottom formulation is addressed in more detail. First, it is shown that in the weakly nonlinear, weakly dispersive regime, the above system of three equations can be reduced to a system of two equations. Second, by combining the novel non-local formulation of the above authors with conformal mappings, it is shown that in the two-dimensional case, it is possible to obtain a system of two equations without any asymptotic approximations. Furthermore, for the weakly nonlinear, weakly dispersive regime, the nonlinear equations are simpler than the equations obtained without conformal mappings, since they contain lower order derivatives for the terms involving the bottom variable.

Conformal mappings in the problem of water-waves/floating-bodies interaction

2007 ◽  
Vol 142 (6) ◽  
pp. 2589-2596
Author(s):  
N. G. Kuznetsov
Keyword(s):  
Water Waves ◽  
Conformal Mappings ◽  
Floating Bodies

Mean Flux in the Tree Surface Zone of Water Waves in a Closed Wave Flume

1995 ◽  
Author(s):  
Witold Cieślikiewicz ◽  
Ove T. Gudmestad
Keyword(s):  
Water Waves ◽  
Surface Zone ◽  
Wave Flume

Time and Frequency Domain Analyses of Shallow Water Waves on a Slope

1991 ◽  
Author(s):  
D H Swart ◽  
J B Crowley
Keyword(s):  
Shallow Water ◽  
Frequency Domain ◽  
Water Waves ◽  
Shallow Water Waves

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

Quality Improvement of X-ray CT Images by Estimation of the Mechanical Misalignment in a Projection Image Using an Iterative Method

2017 ◽  
Vol 137 (3) ◽  
pp. 213-219
Author(s):  
Kenji Noguchi ◽  
Satoshi Takahashi ◽  
Daisuke Suzuki ◽  
Atsushi Teramoto
Keyword(s):  
Quality Improvement ◽  
Iterative Method ◽  
Ct Images ◽  
X Ray ◽  
Projection Image

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

THE REALIZATION OF THE ITERATIVE METHOD OF THE LEAST SQUARES FOR THE ESTIMATION OF STATIC OBJECT PARAMETERS IN MATLAB ENVIRONMENT

2017 ◽  
pp. 28-36
Author(s):  
Galina Vasil’evna Troshina ◽  
Alexander Aleksandrovich Voevoda
Keyword(s):  
Parameter Estimation ◽  
Iterative Method ◽  
Least Squares ◽  
Input Signal ◽  
Layer Structure ◽  
Estimation Procedure ◽  
Parameter Estimation Procedure ◽  
Noise Simulation ◽  
Static Object ◽  
Object Parameters

It was suggested to use the system model working in real time for an iterative method of the parameter estimation. It gives the chance to select a suitable input signal, and also to carry out the setup of the object parameters. The object modeling for a case when the system isn't affected by the measurement noises, and also for a case when an object is under the gaussian noise was executed in the MatLab environment. The superposition of two meanders with different periods and single amplitude is used as an input signal. The model represents the three-layer structure in the MatLab environment. On the most upper layer there are units corresponding to the simulation of an input signal, directly the object, the unit of the noise simulation and the unit for the parameter estimation. The second and the third layers correspond to the simulation of the iterative method of the least squares. The diagrams of the input and the output signals in the absence of noise and in the presence of noise are shown. The results of parameter estimation of a static object are given. According to the results of modeling, the algorithm works well even in the presence of significant measurement noise. To verify the correctness of the work of an algorithm the auxiliary computations have been performed and the diagrams of the gain behavior amount which is used in the parameter estimation procedure have been constructed. The entry conditions which are necessary for the work of an iterative method of the least squares are specified. The understanding of this algorithm functioning principles is a basis for its subsequent use for the parameter estimation of the multi-channel dynamic objects.

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