scholarly journals Comment on “Traveling wave solution of the Boussinesq equation for groundwater flow in horizontal aquifers” by H. A. Basha

2014 ◽  
Vol 50 (9) ◽  
pp. 7527-7528 ◽  
Author(s):  
Jeffrey Olsen ◽  
Jeff Mortensen ◽  
Aleksey S. Telyakovskiy
Keyword(s):  
Groundwater Flow ◽  
Traveling Wave ◽  
Wave Solution ◽  
Boussinesq Equation ◽  
Traveling Wave Solution

Traveling Wave Solution of (2+1) Dimensional Boussinesq Equation by Bernoulli Sub-ODE Method

2011 ◽  
Vol 403-408 ◽  
pp. 202-206
Author(s):  
Qing Hua Feng ◽  
Tong Bo Liu
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Boussinesq Equation ◽  
Expansion Method ◽  
Traveling Wave Solution ◽  
Ode Method

In this paper, we derive exact traveling wave soluti-ons of (2+1) dimensional Boussinesq equation by the known (G’/G) expansion method and a proposed Bernoulli sub-ODE method. We also make a comparison between the two method.

scholarly journals EXACT TRAVELING-WAVE SOLUTION FOR LOCAL FRACTIONAL BOUSSINESQ EQUATION IN FRACTAL DOMAIN

Fractals ◽  
2017 ◽  
Vol 25 (04) ◽  
pp. 1740006 ◽  
Author(s):  
XIAO-JUN YANG ◽  
J. A. TENREIRO MACHADO ◽  
DUMITRU BALEANU
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Boussinesq Equation ◽  
Special Functions ◽  
Traveling Wave Solution ◽  
Nonlinear Pdes ◽  
Type Model ◽  
Fractal Domains ◽  
Fractal Domain ◽  
Exact Traveling Wave Solution

The new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains.

scholarly journals Single peaked traveling wave solutions to a generalized μ-Novikov Equation

2020 ◽  
Vol 10 (1) ◽  
pp. 66-75
Author(s):  
Byungsoo Moon
Keyword(s):  
Linear Combination ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Solutions ◽  
Quadratic Nonlinearities ◽  
Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

Periodic traveling-wave solution of the Sakuma-Nishiguchi equation

1996 ◽  
Vol 54 (19) ◽  
pp. 13484-13486 ◽  
Author(s):  
David R. Rowland ◽  
Zlatko Jovanoski
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solution ◽  
Periodic Traveling Wave

scholarly journals Stability Analysis of an Age-Structured SEIRS Model with Time Delay

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 455 ◽  
Author(s):  
Zhe Yin ◽  
Yongguang Yu ◽  
Zhenzhen Lu
Keyword(s):  
Time Delay ◽  
Equilibrium Point ◽  
Traveling Wave ◽  
Wave Solution ◽  
Disease Model ◽  
Endemic Equilibrium ◽  
Traveling Wave Solution ◽  
Age Structured ◽  
Nonlinear Autonomous System ◽  
Disease Free

This paper is concerned with the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the model. Furthermore, the local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection-induced disease model is established. Finally, some numerical simulations were carried out to illustrate our theoretical results.

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