Nonlinear Partial Differential Equation for Unsteady Vertical Distribution of Suspended Sediments in Open Channel Flows: Effects of Hindered Settling and Concentration-Dependent Mixing Length

2022 ◽  
Vol 148 (1) ◽  
Koeli Ghoshal ◽  
Punit Jain ◽  
Rafik Absi
2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Hasibun Naher ◽  
Farah Aini Abdullah ◽  
M. Ali Akbar

We construct new analytical solutions of the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

1978 ◽  
Vol 1 (4) ◽  
pp. 401-405
Richard Bellman

The purpose of this paper is to derive a nonlinear partial differential equation for whichλgiven by (1.3), is one value of the solution. In Section 2, we derive this equation using a straightforward dynamic programming approach. In Section 3, we discuss some computational aspects of derermining the solution of this equation. In Section 4, we show that the same method may be applied to the nonlinear characteristic value problem. In Section 5, we discuss how the method may by applied to find the higher characteristic values. In Section 5, we discuss how the same method may be applied to some matrix problems. Finally, in Section 7, we discuss selective computation.

2012 ◽  
Vol 09 (01) ◽  
pp. 1250008 ◽  

Para-Hermite–Einstein spacetimes are considered. It is shown that any para-Hermite–Einstein metric is locally defined by one nonlinear partial differential equation of the second order for one function.

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
I. Rusagara ◽  
C. Harley

The temperature profile for fins with temperature-dependent thermal conductivity and heat transfer coefficients will be considered. Assuming such forms for these coefficients leads to a highly nonlinear partial differential equation (PDE) which cannot easily be solved analytically. We establish a numerical balance rule which can assist in getting a well-balanced numerical scheme. When coupled with the zero-flux condition, this scheme can be used to solve this nonlinear partial differential equation (PDE) modelling the temperature distribution in a one-dimensional longitudinal triangular fin without requiring any additional assumptions or simplifications of the fin profile.

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Taha Aziz ◽  
A. Fatima ◽  
F. M. Mahomed

This study focuses on obtaining a new class of closed-form shock wave solution also known as soliton solution for a nonlinear partial differential equation which governs the unsteady magnetohydrodynamics (MHD) flow of an incompressible fourth grade fluid model. The travelling wave symmetry formulation of the model leads to a shock wave solution of the problem. The restriction on the physical parameters of the flow problem also falls out naturally in the course of derivation of the solution.

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Min Wu ◽  
Yousheng Wu

This paper investigates the asymptotic behavior of weak solutions to the generalized nonlinear partial differential equation model. It is proved that every perturbed weak solution of the perturbed generalized nonlinear partial differential equations asymptotically converges to the solution of the original system under the large perturbation.

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