scholarly journals Single solitary wave and wave generation solutions of the Regularised Long Wave (RLW) equation

2021 ◽  
Author(s):  
Ali BAŞHAN
Keyword(s):  
Solitary Wave ◽  
Wave Generation ◽  
Long Wave ◽  
Rlw Equation

scholarly journals Lie Symmetry Analysis and Explicit Solutions for the Time-Fractional Regularized Long-Wave Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Nisrine Maarouf ◽  
Hicham Maadan ◽  
Khalid Hilal
Keyword(s):  
Vector Fields ◽  
Group Analysis ◽  
Power Series Expansion ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Visual Interpretation ◽  
Long Wave ◽  
Rlw Equation ◽  
Regularized Long Wave Equation ◽  
Liouville Fractional Derivative

This paper systematically investigates the Lie group analysis method of the time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions of the time-fractional (RLW) equation are obtained. It is shown that the governing equation can be transformed into a fractional ordinary differential equation with a new independent variable, where the fractional derivatives are in Erdèlyi–Kober sense. Furthermore, the explicit analytic solutions of the time-fractional (RLW) equation are obtained using the power series expansion method. Finally, some graphical features were presented to give a visual interpretation of the solutions.

Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation

2019 ◽  
Vol 340 ◽  
pp. 84-100 ◽  
Author(s):  
B. Wongsaijai ◽  
T. Mouktonglang ◽  
N. Sukantamala ◽  
K. Poochinapan
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Compact Structure ◽  
Structure Preserving ◽  
Rlw Equation

Lump and interactional solutions of the (2+1)-dimensional generalized breaking soliton equation

2019 ◽  
Vol 34 (03) ◽  
pp. 2050037
Author(s):  
Yu-Pei Fan ◽  
Ai-Hua Chen
Keyword(s):  
Solitary Wave ◽  
Asymptotic Analysis ◽  
Bilinear Form ◽  
Lump Solution ◽  
Soliton Equation ◽  
Long Wave ◽  
Wave Limit

In this paper, by using the long wave limit method, we study lump solution and interactional solution of the (2[Formula: see text]+[Formula: see text]1)-dimensional generalized breaking soliton equation without using bilinear form. The moving properties of the lump solution, and the interactional properties of a lump and a solitary wave, are analyzed theoretically and graphically with asymptotic analysis.

Solitary wave solutions, lump solutions and interactional solutions to the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation

2020 ◽  
Vol 34 (07) ◽  
pp. 2050053
Author(s):  
Min Gao ◽  
Hai-Qiang Zhang
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solution ◽  
Lump Solution ◽  
Solitary Wave Solutions ◽  
Bilinear Method ◽  
Long Wave ◽  
Petviashvili Equation ◽  
Dimensional Equation ◽  
Hirota Bilinear ◽  
Bkp Equation

In this paper, we investigate a [Formula: see text]-dimensional B-type Kadomtsev-Petviashvili (BKP) equation, which is a generalization of the [Formula: see text]-dimensional equation. Based on the Hirota bilinear method and the limit technique of long wave, we systematically construct a family of exact solutions of BKP equation including the [Formula: see text]-solitary wave solution, lump solution as well as interaction solution between lump waves and solitary waves.

Radiation of short waves from the resonantly excited capillary–gravity waves

2016 ◽  
Vol 810 ◽  
pp. 5-24 ◽  
Author(s):  
M. Hirata ◽  
S. Okino ◽  
H. Hanazaki
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Gravity Waves ◽  
Wave Pattern ◽  
Short Wave ◽  
Bond Number ◽  
Linear Wave ◽  
Cnoidal Wave ◽  
Short Waves ◽  
Long Wave

Capillary–gravity waves resonantly excited by an obstacle (Froude number: $Fr=1$) are investigated by the numerical solution of the Euler equations. The radiation of short waves from the long nonlinear waves is observed when the capillary effects are weak (Bond number: $Bo<1/3$). The upstream-advancing solitary wave radiates a short linear wave whose phase velocity is equal to the solitary waves and group velocity is faster than the solitary wave (soliton radiation). Therefore, the short wave is observed upstream of the foremost solitary wave. The downstream cnoidal wave also radiates a short wave which propagates upstream in the depression region between the obstacle and the cnoidal wave. The short wave interacts with the long wave above the obstacle, and generates a second short wave which propagates downstream. These generation processes will be repeated, and the number of wavenumber components in the depression region increases with time to generate a complicated wave pattern. The upstream soliton radiation can be predicted qualitatively by the fifth-order forced Korteweg–de Vries equation, but the equation overestimates the wavelength since it is based on a long-wave approximation. At a large Bond number of $Bo=2/3$, the wave pattern has the rotation symmetry against the pattern at $Bo=0$, and the depression solitary waves propagate downstream.

scholarly journals Internal breather-like wave generation by the second mode solitary wave interaction with a step

2016 ◽  
Vol 28 (11) ◽  
pp. 116602 ◽  
Author(s):  
Kateryna Terletska ◽  
Kyung Tae Jung ◽  
Tatiana Talipova ◽  
Vladimir Maderich ◽  
Igor Brovchenko ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Wave Interaction ◽  
Wave Generation ◽  
Second Mode ◽  
Solitary Wave Interaction

Calculations of the development of an undular bore

1966 ◽  
Vol 25 (2) ◽  
pp. 321-330 ◽  
Author(s):  
D. H. Peregrine
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Solitary Wave ◽  
Equations Of Motion ◽  
Experimental Measurements ◽  
Order Of Approximation ◽  
Undular Bore ◽  
Finite Difference Approximations ◽  
Difference Approximations ◽  
Long Wave

If a long wave of elevation travels in shallow water it steepens and forms a bore. The bore is undular if the change in surface elevation of the wave is less than 0·28 of the original depth of water. This paper describes the growth of an undular bore from a long wave which forms a gentle transition between a uniform flow and still water. A physical account of its development is followed by the results of numerical calculations. These use finite-difference approximations to the partial differential equations of motion. The equations of motion are of the same order of approximation as is necessary to derive the solitary wave. The results are in general agreement with the available experimental measurements.

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