Analytical Study on the Generalized Fifth-order Kaup–Kupershmidt Equation From the Shallow Water Wave

2020 ◽  
Vol 60 (9) ◽  
pp. 1533-1533
Author(s):  
Pan Wang ◽  
Jian-Rong Yang ◽  
Li Chen ◽  
Sheng-Xin Li ◽  
Feng-Hua Qi
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Analytical Study ◽  
Shallow Water Wave ◽  
Fifth Order

Analytical Study on the Generalized Fifth-Order Kaup–Kupershmidt Equation from the Shallow Water Wave

2020 ◽  
Vol 60 (9) ◽  
pp. 1480-1487
Author(s):  
Pan Wang ◽  
Jian-Rong Yang ◽  
Li Chen ◽  
Sheng-Xin Li ◽  
Feng-Hua Qi
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Analytical Study ◽  
Shallow Water Wave ◽  
Fifth Order

SOLITONIC INVESTIGATION ON THE GENERAL FIFTH-ORDER SHALLOW WATER WAVE MODELS

2001 ◽  
Vol 12 (06) ◽  
pp. 879-888 ◽  
Author(s):  
YI-TIAN GAO ◽  
BO TIAN
Keyword(s):  
Shallow Water ◽  
Symbolic Computation ◽  
Water Wave ◽  
Bäcklund Transformations ◽  
Shallow Water Wave ◽  
Backlund Transformations ◽  
Wave Models ◽  
Fifth Order

For the general fifth-order shallow water wave models, we perform computerized symbolic computation to obtain two auto-Bäcklund transformations and four families of the bell-shaped solitonic solutions, which are exact analytic.

Dynamics of Combined Solitary-waves in the General Shallow Water Wave Models

2003 ◽  
Vol 58 (9-10) ◽  
pp. 520-528
Author(s):  
Woo-Pyo Hong
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Wave ◽  
Hyperbolic Function ◽  
Ansatz Method ◽  
Shallow Water Wave ◽  
Wave Models ◽  
Fifth Order ◽  
52.35 Mw

We find new analytic solitary-wave solutions, having a nonzero background at infinity, of the general fifth-order shallow water wave models using the hyperbolic function ansatz method. We study the dynamical properties of the solutions in the combined form of a bright and a dark solitary-wave by using numerical simulations. It is shown that the solitary-waves can be stable or marginally stable, depending on the coefficients of the model.We study the interaction dynamics by using the combined solitary-waves as the initial profiles to show the formation of sech2-type solitary-waves in the presence of a strong nonlinear dispersion term. - PACS: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw

scholarly journals Dynamics of Bright Solitary-waves in a General Fifth-order Shallow Water-wave Model

2004 ◽  
Vol 59 (4-5) ◽  
pp. 257-265
Author(s):  
Woo-Pyo Hong
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Wave ◽  
Wave Model ◽  
Wave Number ◽  
Solitary Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Fifth Order

New analytic sech2-type traveling solitary-wave solutions, satisfying zero background at infinity, of a general fifth-order shallow water-wave model are found and compared with previously obtained non-zero background solutions. The allowed coefficient regions for the solitary-wave solutions are classified by requiring the wave number and angular frequency to be real. Detailed numerical simulations are performed to demonstrate the stability of the solitary-waves and to show the soliton-like behavior of two interacting solitary-waves. For a large nonlinear term we show the formation of a bounded state of two solitary-waves, called bion, which travels as a single coherent structure. - PACS numbers: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw

scholarly journals Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1439
Author(s):  
Chaudry Masood Khalique ◽  
Karabo Plaatjie
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Elliptic Integral ◽  
Momentum Conservation ◽  
Two Dimensional ◽  
Order Ordinary Differential Equation ◽  
Closed Form Solutions ◽  
Shallow Water Wave

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

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