Propagation of quasiplane nonlinear waves in tubes and the approximate solutions of the generalized Burgers equation

2002 ◽  
Vol 112 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Michal Bednarik ◽  
Petr Konicek
Keyword(s):  
Nonlinear Waves ◽  
Burgers Equation ◽  
Approximate Solutions ◽  
Generalized Burgers Equation

scholarly journals Propagation of Quasi-plane Nonlinear Waves in Tubes

10.14311/368 ◽  
2002 ◽  
Vol 42 (4) ◽  
Author(s):  
P. Koníček ◽  
M. Bednařík ◽  
M. Červenka
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Nonlinear Waves ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Circular Duct ◽  
Generalized Burgers Equation ◽  
Kzk Equation ◽  
Model Equations ◽  
Diffraction Effects

This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicability of the KZK equation and the GBE equation for describing nonlinear waves in tubes are discussed.

scholarly journals A new variation for the relativistic Euler equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mahmoud A. E. Abdelrahman ◽  
Hanan A. Alkhidhr
Keyword(s):  
Euler Equations ◽  
Nonlinear Waves ◽  
Approximation Scheme ◽  
Strength Function ◽  
Convergent Sequence ◽  
Approximate Solutions ◽  
Large Initial Data ◽  
Initial Value ◽  
Relativistic Euler Equations ◽  
Glimm Scheme

Abstract The Glimm scheme is one of the so famous techniques for getting solutions of the general initial value problem by building a convergent sequence of approximate solutions. The approximation scheme is based on the solution of the Riemann problem. In this paper, we use a new strength function in order to present a new kind of total variation of a solution. Based on this new variation, we use the Glimm scheme to prove the global existence of weak solutions for the nonlinear ultra-relativistic Euler equations for a class of large initial data that involve the interaction of nonlinear waves.

1-Soliton solution of the generalized Burgers equation with generalized evolution

2011 ◽  
Vol 217 (24) ◽  
pp. 10289-10294 ◽  
Author(s):  
Anjan Biswas ◽  
Houria Triki ◽  
T. Hayat ◽  
Omar M. Aldossary
Keyword(s):  
Soliton Solution ◽  
Burgers Equation ◽  
Generalized Burgers Equation

SOLVING THE GENERALIZED BURGERS–KdV EQUATION BY A COMBINATION METHOD

2008 ◽  
Vol 22 (21) ◽  
pp. 2021-2025 ◽  
Author(s):  
YUANXI XIE
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Combination Method ◽  
Generalized Kdv Equation ◽  
Generalized Burgers Equation

In view of the analysis on the characteristics of the generalized Burgers equation, generalized KdV equation and generalized Burgers–KdV equation, a combination method is presented to seek the explicit and exact solutions to the generalized Burgers–KdV equation by combining with those of the generalized Burgers equation and generalized KdV equation. As a result, many explicit and exact solutions for the generalized Burgers–KdV equation are successfully obtained by this technique.

Higher Order Solution of Nonlinear Waves. II. Shock Wave Described by Burgers Equation

1997 ◽  
Vol 66 (4) ◽  
pp. 984-987 ◽  
Author(s):  
Shinsuke Watanabe ◽  
Shingo Ishiwata ◽  
Katsuyuki Kawamura ◽  
Heung Geun Oh
Keyword(s):  
Shock Wave ◽  
Nonlinear Waves ◽  
Burgers Equation ◽  
Higher Order ◽  
Order Solution
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