Decay of solutions to a water wave model with a nonlocal viscous term

2020 ◽  
Vol 31 (1) ◽  
pp. 115-127
Author(s):  
S. Dumont ◽  
O. Goubet ◽  
I. Manoubi
Keyword(s):  
Water Wave ◽  
Wave Model ◽  
Viscous Term ◽  
Decay Of Solutions

scholarly journals Decay of solutions to a water wave model with a nonlocal viscous dispersive term

2010 ◽  
Vol 27 (4) ◽  
pp. 1473-1492 ◽  
Author(s):  
Min Chen ◽  
◽  
S. Dumont ◽  
Louis Dupaigne ◽  
Olivier Goubet ◽  
...  
Keyword(s):  
Water Wave ◽  
Wave Model ◽  
Decay Of Solutions ◽  
Dispersive Term

Theoretical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach

2017 ◽  
Vol 8 (1) ◽  
pp. 253-266 ◽  
Author(s):  
Olivier Goubet ◽  
Imen Manoubi
Keyword(s):  
Theoretical Analysis ◽  
Water Wave ◽  
Wave Model ◽  
Order Derivative ◽  
Asymptotic Convergence ◽  
Well Posedness ◽  
Viscous Term ◽  
Dispersive Term

Abstract In this paper, we study the following water wave model with a nonlocal viscous term: u_{t}+u_{x}+\beta u_{xxx}+\frac{\sqrt{\nu}}{\sqrt{\pi}}\frac{\partial}{% \partial t}\int_{0}^{t}\frac{u(s)}{\sqrt{t-s}}\,ds+uu_{x}=\nu u_{xx}, where {\frac{1}{\sqrt{\pi}}\frac{\partial}{\partial t}\int_{0}^{t}\frac{u(s)}{\sqrt{% t-s}}\,ds} is the Riemann–Liouville half-order derivative. We prove the well-posedness of this model using diffusive realization of the half-order derivative, and we discuss the asymptotic convergence of the solution. Also, we compare our mathematical results with those given in [5] and [14] for similar equations.

Landslide Generated Water Wave Model

1976 ◽  
Vol 102 (9) ◽  
pp. 1269-1282
Author(s):  
Donald C. Raney ◽  
H. Lee Butler
Keyword(s):  
Water Wave ◽  
Wave Model

Multiple soliton, fusion, breather, lump, mixed kink-lump and periodic solutions to the extended shallow water wave model in (2+1)-dimensions

2020 ◽  
pp. 2150138
Author(s):  
Hajar F. Ismael ◽  
Aly Seadawy ◽  
Hasan Bulut
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Soliton Solutions ◽  
Quadratic Function ◽  
Wave Model ◽  
Simple Method ◽  
Shallow Water Wave ◽  
Hirota Bilinear Form ◽  
The One ◽  
Physical Phenomena

In this paper, we consider the shallow water wave model in the (2+1)-dimensions. The Hirota simple method is applied to construct the new dynamics one-, two-, three-, [Formula: see text]-soliton solutions, complex multi-soliton, fusion, and breather solutions. By using the quadratic function, the one-lump, mixed kink-lump and periodic lump solutions to the model are obtained. The Hirota bilinear form variable of this model is derived at first via logarithmic variable transform. The physical phenomena to this model are explored. The obtained results verify the proposed model.

Sign in / Sign up

Export Citation Format

Share Document