Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method

1986 ◽  
Vol 166 (-1) ◽  
pp. 189 ◽  
Author(s):  
Hiroshi Kagemoto ◽  
Dick K. P. Yue
Keyword(s):  
Water Waves ◽  
Three Dimensional ◽  
Algebraic Method

Diverse wave propagation in shallow water waves with the Kadomtsev–Petviashvili–Benjamin–Bona–Mahony and Benney–Luke integrable models

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 808-818
Author(s):  
Usman Younas ◽  
Aly R. Seadawy ◽  
Muhammad Younis ◽  
Syed T. R. Rizvi ◽  
Saad Althobaiti
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Three Dimensional ◽  
Wave Model ◽  
Algebraic Method ◽  
Integrable Models ◽  
Computational Technique ◽  
Shallow Water Waves ◽  
Physical Problems ◽  
Contour Plots

Abstract The shallow water wave model is one of the completely integrable models illustrating many physical problems. In this article, we investigate new exact wave structures to Kadomtsev–Petviashvili–Benjamin–Bona–Mahony and the Benney–Luke equations which explain the behavior of waves in shallow water. The exact structures are expressed in the shapes of hyperbolic, singular periodic, rational as well as solitary, singular, shock, shock-singular solutions. An efficient computational strategy namely modified direct algebraic method is employed to construct the different shapes of wave structures. Moreover, by fixing parameters, the graphical representations of some solutions are plotted in terms of three-dimensional, two-dimensional and contour plots, which explain the physical movement of the attained results. The accomplished results show that the applied computational technique is valid, proficient, concise and can be applied in more complicated phenomena.

scholarly journals Optical Solutions of the Date–Jimbo–Kashiwara–Miwa Equation via the Extended Direct Algebraic Method

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Ghazala Akram ◽  
Naila Sajid ◽  
Muhammad Abbas ◽  
Y. S. Hamed ◽  
Khadijah M. Abualnaja
Keyword(s):  
Water Waves ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Mathematical Physics ◽  
Integration Scheme ◽  
Hyperbolic Functions ◽  
Dynamical Characteristics ◽  
Complex Valued ◽  
Djkm Equation ◽  
Model Water

In this study, the solutions of 2 + 1 -dimensional nonlinear Date–Jimbo–Kashiwara–Miwa (DJKM) equation are characterized, which can be used in mathematical physics to model water waves with low surface tension and long wavelengths. The integration scheme, namely, the extended direct algebraic method, is used to extract complex trigonometric, rational and hyperbolic functions. The complex-valued solutions represent traveling waves in different structures, such as bell-, V-, and W-shaped multiwaves. The results obtained in this article are novel and more general than those contained in the literature (Wang et al., 2014, Yuan et al., 2017, Pu and Hu 2019, Singh and Gupta 2018). Furthermore, the mechanical features and dynamical characteristics of the obtained solutions are demonstrated by three-dimensional graphics.

Nonlinear dynamical wave structures to the Date–Jimbo–Kashiwara–Miwa equation and its modulation instability analysis

2021 ◽  
pp. 2150300
Author(s):  
M. Younis ◽  
A. R. Seadawy ◽  
M. Bilal ◽  
S. T. R. Rizvi ◽  
Saad Althobaiti ◽  
...  
Keyword(s):  
Function Method ◽  
Modulation Instability ◽  
Existence Of Solutions ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Two Dimensional ◽  
Instability Analysis ◽  
Nonlinear Dynamical ◽  
Wave Solutions ◽  
Different Shapes

A particular attention is paid to the nonlinear dynamical exact wave solutions to the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation (DJKME). A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing [Formula: see text]-expansion function method and modified direct algebraic method. In addition, we also secure singular periodic and plane wave solutions with arbitrary parameters. We also discussed the modulation instability analysis of the governing model. The constraint conditions for the validity of existence of solutions are also reported. Moreover, three-dimensional and two-dimensional, and their corresponding contour graphs are sketched for a better understanding of the derived solutions with the values of arbitrary parameters.

Numerical Calculation of the Wave Integrals in the Linearized Theory of Water Waves

1977 ◽  
Vol 21 (01) ◽  
pp. 1-10 ◽  
Author(s):  
Hung-Tao Shen ◽  
Cesar Farell
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Integral Term ◽  
Linearized Theory ◽  
Single Integral ◽  
Numerical Computing ◽  
Complex Exponential ◽  
Derivatives Of

A method for the numerical evaluation of the derivatives of the linearized velocity potential for three-dimensional flow past a unit source submerged in a uniform stream is presented together with a discussion of existing techniques. It is shown in particular that calculation of the double integral term in these functions can be efficiently accomplished in terms of a single integral with the integrand expressed in terms of the complex exponential integral, for which numerical computing techniques are available.

On the subharmonic instabilities of steady three-dimensional deep water waves

1994 ◽  
Vol 262 ◽  
pp. 265-291 ◽  
Author(s):  
Mansour Ioualalen ◽  
Christian Kharif
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Transverse Direction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Two Dimensional ◽  
Wave Steepness ◽  
Oblique Angle

A numerical procedure has been developed to study the linear stability of nonlinear three-dimensional progressive gravity waves on deep water. The three-dimensional patterns considered herein are short-crested waves which may be produced by two progressive plane waves propagating at an oblique angle, γ, to each other. It is shown that for moderate wave steepness the dominant resonances are sideband-type instabilities in the direction of propagation and, depending on the value of γ, also in the transverse direction. It is also shown that three-dimensional progressive gravity waves are less unstable than two-dimensional progressive gravity waves.

NUMERICAL SIMULATION OF THREE DIMENSIONAL TSUNAMIS WATER WAVES GENERATED BY LANDSLIDES: COMPARISON BETWEEN PHYSICAL MODEL RESULTS, VOF AND SPH

2007 ◽  
Author(s):  
Paolo De Girolamo ◽  
Tso-Ren Wu ◽  
Philip L.-F. Liu ◽  
Andrea Panizzo ◽  
Giorgio Bellotti ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Physical Model ◽  
Water Waves ◽  
Three Dimensional
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