Some novel different solutions for Boussinesq-type models including bright, singular, and dark soliton ones

Authors

  • M.T. Darvishi Razi University
  • Mohammad Najafi Razi University
  • Hadi Rezazadeh Amol University of Special Modern Technologies
  • S. Rezapour Azarbaijan Shahid Madani University
  • Mustafa Inc Firat University

DOI:

https://doi.org/10.31349/RevMexFis.70.031306

Keywords:

Boussinesq-type equation; Singular-solution; Dark-soliton solution; Bright-soliton solution

Abstract

Some new different kinds of one-soliton solutions for various forms of Boussinesq-type equations are presented in this
paper to describe the nonlinear wave phenomena in coastal and ocean areas such as tsunami waves. These one-soliton
solutions include bright, dark, and singular ones. The property of each solution in coastal and ocean engineering is
explained.

References

D.H. Peregrine, Long wave on a beach. J. Fluid Mech. 27 (1967) 815-827

C.I. Christov, G.A. Maugin, M.G. Velarde, Well-posed Boussinesq paradigm with purely spatial higher-order derivatives. Phys. Rev. E. 54 (1996) 3621-3638

A. Biswas, D. Milovic, A. Ranasinghe, Solitary waves of Boussinesq equation in a power law media. Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 3738-3742

A.M. Wazwaz, New traveling wave solutions to the Boussinesq and the Klein-Gordon equations. Commun. Nonlinear Sci. Numer. Simul. 13 (2008) 889-901

A.M. Wazwaz, Multiple soliton solutions for an integrable couplings of the Boussinesq equation. Ocean Engineering 73 (2013) 38-40

M.A. Akbar, L. Akinyemi, S.W. Yao, A. Jhangeer, H. Rezazadeh, M.M. Khater, H. Ahmad, M. Inc, Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method. Res. Phys. 25 (2021) 104228. https://doi.org/10.1016/j.rinp.2021.104228

A.M. Wazwaz, Multiple-soliton solutions for the Boussinesq equation. Appl. Math. Comput. 192 (2007) 479-486

A.M. Wazwaz, Solitons and singular solitons for a variety of Boussinesq-like equations. Ocean Engineering 53 (2012) 1–5

P. Daripa, W. Hua, A numerical study of an ill-posed Boussinesq equation arising in water waves and nonlinear lattices: Filtering and regularization techniques. Appl. Math. Comput. 101 (1999) 159–207

D. Adhikari, C. Cao, J. Wu, The 2D Boussinesq equations with vertical viscosity and vertical diffusivity. Journal of Differential Equations 249 (2010) 1078–1088

A. Biswas, Solitary waves for power-law regularized long-wave equation and R(m, n) equation. Nonlinear Dyn. 59 (2010) 423–426

A. Biswas, C.M. Khalique, Stationary solutions for nonlinear dispersive Schrödinger’s equation. Nonlinear Dyn. 63 (2011) 623–626

J.L. Bona, M. Chen, J.-C. Saut, Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory, Nonlinearity 17 (2004) 925

C.I. Christov, G.A. Maugin, M.G. Velarde, Well-posed Boussinesq paradigm with purely spatial higher-order derivatives. Phys. Rev. E 54 (1996) 3621

Z. Huazhi, L. Huajun, L. Xiaodong, L. Aixia, The application of a numerical model to coastal surface water waves. Journal of Ocean University of China 4 (2005) 177

N. Droenen, R. Deigaard, Adaptation of a Boussinesq wave model for Dune erosion modeling. Coastal Engineering Proceedings 1 (2012) 31

J.T. Kirby, Boussinesq models and their application to coastal processes across a wide range of scales. PhD diss., American Society of Civil Engineers, (2016)

P.J. Lynett, J.A. Melby, D.-H Kim, An application of Boussinesq modeling to hurricane wave overtopping and inundation. Ocean Engineering 37 (2010) 135-153

V. Roeber, K.F. Cheung, M.H. Kobayashi, Shock-capturing Boussinesq-type model for nearshore wave processes. Coastal Engineering 57 (2010) 407–423

A.M. Wazwaz, Solitons and singular solitons for a variety of Boussinesq-like equations. Ocean Eng. 53 (2012) 1–5

M.T. Darvishi, M. Najafi, A.M. Wazwaz, Soliton solutions for Boussinesq-like equations with spatio-temporal dispersion. Ocean Eng. 130 (2017) 228–240

M.T. Darvishi, M. Najafi, A.M. Wazwaz, Traveling wave solutions for Boussinesq-like equations with spatial and spatialtemporal dispersion. Rom. Rep. Phys. 70 (2018) 108

A. Nakamura, Simple explode-decay mode solutions of a certain one-space dimensional nonlinear evolution equations. J. Phys. Soc. Japan 33 (1972) 1456-1458

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Published

2024-05-01

How to Cite

[1]
M. Darvishi, M. Najafi, H. Rezazadeh, S. Rezapour, and M. Inc, “Some novel different solutions for Boussinesq-type models including bright, singular, and dark soliton ones”, Rev. Mex. Fís., vol. 70, no. 3 May-Jun, pp. 031306 1–, May 2024.