scholarly journals Numerical Simulations of Modulated Waves in a Higher-Order Dysthe Equation

Water Waves ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 59-77
Author(s):  
Alexey Slunyaev ◽  
Efim Pelinovsky
Keyword(s):  
Numerical Simulations ◽  
Higher Order ◽  
Modulated Waves ◽  
Dysthe Equation

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

scholarly journals Metode Iterasi Tiga Langkah untuk Menyelesaikan Persamaan NonLinear dengan Menggunakan Matlab

2019 ◽  
Vol 4 (2) ◽  
pp. 34
Author(s):  
Deasy Wahyuni ◽  
Elisawati Elisawati
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Iteration Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Convergence Order ◽  
Matlab Program ◽  
Analytical Results

Newton method is one of the most frequently used methods to find solutions to the roots of nonlinear equations. Along with the development of science, Newton's method has undergone various modifications. One of them is the hasanov method and the newton method variant (vmn), with a higher order of convergence. In this journal focuses on the three-step iteration method in which the order of convergence is higher than the three methods. To find the convergence order of the three-step iteration method requires a program that can support the analytical results of both methods. One of them using the help of the matlab program. Which will then be compared with numerical simulations also using the matlab program.  Keywords : newton method, newton method variant, Hasanov Method and order of convergence

scholarly journals WEAKLY NONPARAXIAL EFFECTS ON THE PROPAGATION OF (1+1)D SPATIAL SOLITONS IN INHOMOGENEOUS KERR MEDIA

2005 ◽  
Vol 14 (02) ◽  
pp. 203-219 ◽  
Author(s):  
A. SURYANTO ◽  
E. VAN GROESEN ◽  
M. HAMMER
Keyword(s):  
Wave Equation ◽  
Numerical Simulations ◽  
Beam Propagation ◽  
Bound State ◽  
Higher Order ◽  
Spatial Solitons ◽  
Nls Equation ◽  
Soliton Propagation ◽  
Kerr Media ◽  
Higher Order Terms

The widely-used approach to study the beam propagation in Kerr media is based on the slowly varying envelope approximation (SVEA) which is also known as the paraxial approximation. Within this approximation, the beam evolution is described by the nonlinear Schrödinger (NLS) equation. In this paper, we extend the NLS equation by including higher-order terms to study the effects of nonparaxiality on the soliton propagation in inhomogeneous Kerr media. The result is still a one-way wave equation which means that all back-reflections are neglected. The accuracy of this approximation exceeds the standard SVEA. By performing several numerical simulations, we show that the NLS equation produces reasonably good predictions for relatively small degrees of nonparaxiality, as expected. However, in the regions where the envelope beam is changing rapidly as in the breakup of a multisoliton bound state, the nonparaxiality plays an important role.

scholarly journals Coherent structures in granulation convection and their importance for higher order closure models

2006 ◽  
Vol 2 (S239) ◽  
pp. 74-76 ◽  
Author(s):  
F. Kupka ◽  
F. J. Robinson
Keyword(s):  
Numerical Simulations ◽  
Coherent Structures ◽  
Normal Approximation ◽  
Substantial Improvement ◽  
Higher Order ◽  
Turbulent Convection ◽  
The Sun ◽  
Order Of Magnitude ◽  
Non Local ◽  
Stress Models

AbstractWe use numerical simulations of granulation in the Sun and a K dwarf to study the effects of coherent structures on higher order moments. The latter need to be calculated in non-local Reynolds stress models of turbulent convection. Models that explicitly account for the asymmetry between up- and downflows as well as hot and cold drafts provide a substantial improvement over traditional ones, such as the quasi-normal approximation, which is only able to provide order of magnitude estimates for this type of flow.

Phase Field Dynamic Modelling of Shape Memory Alloys Based on Isogeometric Analysis

2012 ◽  
Vol 78 ◽  
pp. 63-68 ◽  
Author(s):  
Rakesh Dhote ◽  
Hector Gomez ◽  
Roderick Melnik ◽  
Jean Zu
Keyword(s):  
Shape Memory Alloys ◽  
Numerical Simulations ◽  
Shape Memory ◽  
Microstructure Evolution ◽  
Phase Field ◽  
Isogeometric Analysis ◽  
Field Model ◽  
Phase Field Model ◽  
Higher Order ◽  
Martensitic Phase Transformations

Shape Memory Alloys (SMAs) exhibit complex behaviors as a result of their constituent phases and microstructure evolution. In this paper, we focus on the numerical simulations of microstructure evolution in SMAs using a phase-field model for the two dimensional square-to-rectangular martensitic phase transformations. The phase-field model, based on the Ginzburg-Landau theory, has strong non-linearity, thermo-mechanical coupling, and higher-order differential terms and presents substantial challenges for numerical simulations. The isogeometric analysis, developed in this paper using the rich NURBS basis functions, offers several advantages in solving such complex problems with higher-order partial differential equations as the problem at hand. To our best knowledge, we report here for the first time the use of the new method in the study of microstructure evolution in SMAs. The numerical experiments of microstructure evolution have been carried out on the FePd SMA specimen. The results are in good agreement with those previously reported in the literature.

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