Oblique resonance wave phenomena for nonlinear coupled evolution equations with fractional temporal evolution

2019 ◽  
Vol 134 (9) ◽  
Author(s):  
S. Akther ◽  
M. G. Hafez ◽  
F. Ferdous
Keyword(s):  
Evolution Equations ◽  
Temporal Evolution ◽  
Resonance Wave ◽  
Wave Phenomena

scholarly journals Waves, Solids, and Nonlinearities

1995 ◽  
Vol 2 (2) ◽  
pp. 173-190 ◽  
Author(s):  
Jüri Engelbrecht
Keyword(s):  
Mathematical Models ◽  
Evolution Equations ◽  
Constitutive Behavior ◽  
Energy Redistribution ◽  
New Directions ◽  
Basic Concepts ◽  
Complicated Geometry ◽  
Wave Phenomena ◽  
Wave Properties ◽  
Bearing System

In this article nonlinearity is taken as a basic property of continua or any other wave-bearing system. The analysis includes the conventional wave propagation problems and also the wave phenomena that are not described by traditional hyperbolic mathematical models. The basic concepts of continuum mechanics and the possible sources of nonlinearities are briefly discussed. It is shown that the technique of evolution equations leads to physically well-explained results provided the basic models are hyperbolic. Complicated constitutive behavior and complicated geometry lead to mathematical models of different character and, as shown by numerous examples, other methods are then used for the analysis. It is also shown that propagating instabilities possess wave properties and in this case the modeling of energy redistribution has a great importance. Finally, some new directions in the theory and applications are indicated.

scholarly journals Numerical modeling of rogue waves in coastal waters

2013 ◽  
Vol 1 (5) ◽  
pp. 5779-5804
Author(s):  
A. Sergeeva ◽  
A. Slunyaev ◽  
E. Pelinovsky ◽  
T. Talipova ◽  
D.-J. Doong
Keyword(s):  
Nonlinear Waves ◽  
Coastal Waters ◽  
Evolution Equations ◽  
Temporal Evolution ◽  
Rogue Waves ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Waves ◽  
The Mean ◽  
Spatio Temporal ◽  
Reconstructed Time Series

Abstract. The spatio-temporal evolution of rogue waves measured in Taiwanese coastal waters is reconstructed by means of numerical simulations; their lifetimes are estimated at up to 100 s. The reconstructed time series were measured at different locations (with dimensionless depths within the range kh = 1.3 ... 4.0, where k is the wavenumber and h is the depth), but all are surprisingly weakly nonlinear waves. The variable-coefficient approximate evolution equations, which take into account the shoaling effect, allow us to analyze the abnormal wave evolution in essentially non-uniform conditions of real coastal bathymetry. The reconstruction reveals an interesting peculiarity of the coastal rogue events: though the mean wave amplitudes get amplified as waves travel onshore, other rogue waves are likely to occur at deeper locations, but not closer to the coast (the shallowest simulated point is characterized by kh ≈ 0.7).

scholarly journals Abstract Functional Stochastic Evolution Equations Driven by Fractional Brownian Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Mark A. McKibben ◽  
Micah Webster
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Evolution Equations ◽  
Separable Hilbert Space ◽  
Mild Solutions ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Convergence Results ◽  
Real Separable Hilbert Space ◽  
Wave Phenomena

We investigate a class of abstract functional stochastic evolution equations driven by a fractional Brownian motion in a real separable Hilbert space. Global existence results concerning mild solutions are formulated under various growth and compactness conditions. Continuous dependence estimates and convergence results are also established. Analysis of three stochastic partial differential equations, including a second-order stochastic evolution equation arising in the modeling of wave phenomena and a nonlinear diffusion equation, is provided to illustrate the applicability of the general theory.

Abundant fractional solitons to the coupled nonlinear Schrödinger equations arising in shallow water waves

2020 ◽  
Vol 34 (18) ◽  
pp. 2050162
Author(s):  
N. Raza ◽  
M. H. Rafiq
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Temporal Evolution ◽  
Soliton Solutions ◽  
Unified Approach ◽  
Shallow Water Waves ◽  
Wave Phenomena ◽  
Group Velocities ◽  
Fractional Parameter ◽  
Monochromatic Waves

In this work, the dynamics of wave phenomena modeled by (2[Formula: see text]+[Formula: see text]1)-dimensional coupled nonlinear Schrodinger’s equations with fractional temporal evolution is studied. The solutions of the equations are two monochromatic waves with nonlinear modulations that have almost identical group velocities. The unified approach along with the properties of the local M-derivative are used to obtain dark and rational soliton solutions. The restrictions on parameters ensure that these soliton solutions are persevering. Lastly, the influence of the fractional parameter upon the obtained results are evaluated and depicted through graphs.

The nonlinear temporal evolution of a disturbance to a stratified mixing layer

1995 ◽  
Vol 291 ◽  
pp. 287-297 ◽  
Author(s):  
Roland Mallier
Keyword(s):  
Evolution Equations ◽  
Temporal Evolution ◽  
Nonlinear Evolution ◽  
Mixing Layer ◽  
Nonlinear Evolution Equations ◽  
Critical Layer ◽  
Instability Wave ◽  
Layer Analysis ◽  
Order Of Magnitude ◽  
Dimensional Instability

Using a nonlinear critical layer analysis, Goldstein & Leib (1988) derived a set of nonlinear evolution equations governing the spatial growth of a two-dimensional instability wave on a homogeneous incompressible tanh y mixing layer. In this study, we extend this analysis to the temporal growth of the García model of an incompressible stratified shear layer. We consider the stage of the evolution in which the growth first becomes nonlinear, with the nonlinearity appearing inside the critical layer. The Reynolds number is assumed to be just large enough so that the unsteady, nonlinear and viscous terms all enter at the same order of magnitude inside the critical layer. The equations are solved numerically for the inviscid case.

scholarly journals Explicit Wave Phenomena to the Couple Type Fractional Order Nonlinear Evolution Equations

2021 ◽  
pp. 104597
Author(s):  
M. Ayesha Khatun ◽  
Mohammad Asif Arefin ◽  
M. Hafiz Uddin ◽  
Dumitru Baleanu ◽  
M. Ali Akbar ◽  
...  
Keyword(s):  
Fractional Order ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Wave Phenomena

scholarly journals High-resolution spectropolarimetric observations of the temporal evolution of magnetic fields in photospheric bright points

2020 ◽  
Vol 633 ◽  
pp. A60
Author(s):  
P. H. Keys ◽  
A. Reid ◽  
M. Mathioudakis ◽  
S. Shelyag ◽  
V. M. J. Henriques ◽  
...  
Keyword(s):  
High Resolution ◽  
Feature Tracking ◽  
Temporal Evolution ◽  
Simulated Data ◽  
Lower Atmosphere ◽  
Small Scale ◽  
Magnetic Elements ◽  
Disc Centre ◽  
Wave Phenomena ◽  
Field Strengths

Context. Magnetic bright points (MBPs) are dynamic, small-scale magnetic elements often found with field strengths of the order of a kilogauss within intergranular lanes in the photosphere. Aims. Here we study the evolution of various physical properties inferred from inverting high-resolution full Stokes spectropolarimetry data obtained from ground-based observations of the quiet Sun at disc centre. Methods. Using automated feature-tracking algorithms, we studied 300 MBPs and analysed their temporal evolution as they evolved to kilogauss field strengths. These properties were inferred using both the NICOLE and SIR Stokes inversion codes. We employ similar techniques to study radiative magnetohydrodynamical simulations for comparison with our observations. Results. Evidence was found for fast (∼30−100 s) amplification of magnetic field strength (by a factor of 2 on average) in MBPs during their evolution in our observations. Similar evidence for the amplification of fields is seen in our simulated data. Conclusions. Several reasons for the amplifications were established, namely, strong downflows preceding the amplification (convective collapse), compression due to granular expansion and mergers with neighbouring MBPs. Similar amplification of the fields and interpretations were found in our simulations, as well as amplification due to vorticity. Such a fast amplification will have implications for a wide array of topics related to small-scale fields in the lower atmosphere, particularly with regard to propagating wave phenomena in MBPs.

scholarly journals Numerical modeling of rogue waves in coastal waters

2014 ◽  
Vol 14 (4) ◽  
pp. 861-870 ◽  
Author(s):  
A. Sergeeva ◽  
A. Slunyaev ◽  
E. Pelinovsky ◽  
T. Talipova ◽  
D.-J. Doong
Keyword(s):  
Numerical Modeling ◽  
Coastal Waters ◽  
Variable Coefficient ◽  
Evolution Equations ◽  
Temporal Evolution ◽  
Rogue Waves ◽  
Wave Number ◽  
Weakly Nonlinear ◽  
The Mean ◽  
Spatio Temporal

Abstract. Spatio-temporal evolution of rogue waves measured in Taiwanese coastal waters is reconstructed by means of numerical simulations. Their lifetimes are up to 100 s. The time series used for reconstructions were measured at dimensionless depths within the range of kh = 1.3–4.0, where k is the wave number and h is the depth. All identified rogue waves are surprisingly weakly nonlinear. The variable-coefficient approximate evolution equations, which take into account the shoaling effect, allow us to analyze the abnormal wave evolution over non-uniform real coastal bathymetry. The shallowest simulated point is characterized by kh ≈ 0.7. The reconstruction reveals an interesting peculiarity of the coastal rogue events: though the mean wave amplitudes increase as waves travel onshore, rogue waves are likely to occur at deeper locations, but not closer to the coast.

Fundamentals of Wave Phenomena

2010 ◽  
Author(s):  
Akira Hirose ◽  
Karl E. Lonngren
Keyword(s):  
Wave Phenomena
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