Traveling wave solutions of the one-dimensional Boussinesq paradigm equation

2013 ◽  
Author(s):  
V. M. Vassilev ◽  
P. A. Djondjorov ◽  
M. Ts. Hadzhilazova ◽  
I. M. Mladenov
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
One Dimensional ◽  
Wave Solutions ◽  
The One

EXACT TRAVELING-WAVE SOLUTIONS FOR ONE-DIMENSIONAL MODIFIED KORTEWEG–DE VRIES EQUATION DEFINED ON CANTOR SETS

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940010 ◽  
Author(s):  
FENG GAO ◽  
XIAO-JUN YANG ◽  
YANG JU
Keyword(s):  
Traveling Wave ◽  
Vries Equation ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Cantor Sets ◽  
Wave Transformation ◽  
One Dimensional ◽  
Wave Solutions ◽  
De Vries ◽  
The One

The one-dimensional modified Korteweg–de Vries equation defined on a Cantor set involving the local fractional derivative is investigated in this paper. With the aid of the fractal traveling-wave transformation technology, the nondifferentiable traveling-wave solutions for the problem are discussed in detail. The obtained results are accurate and efficient for describing the fractal water wave in mathematical physics.

scholarly journals Traveling wave solutions for the Richards equation with hysteresis

2019 ◽  
Vol 84 (4) ◽  
pp. 797-812 ◽  
Author(s):  
E El Behi-Gornostaeva ◽  
K Mitra ◽  
B Schweizer
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Richards Equation ◽  
One Dimensional ◽  
Homogeneous Solutions ◽  
Wave Solutions ◽  
Relevant Effect ◽  
Saturation Overshoot ◽  
The One

Abstract We investigate the one-dimensional non-equilibrium Richards equation with play-type hysteresis. It is known that regularized versions of this equation permit traveling wave solutions that show oscillations and, in particular, the physically relevant effect of a saturation overshoot. We investigate here the non-regularized hysteresis operator and combine it with a positive $\tau $-term. Our result is that the model has monotone traveling wave solutions. These traveling waves describe the behavior of fronts in a bounded domain. In a two-dimensional interpretation, the result characterizes the speed of fingers in non-homogeneous solutions.

Multiple wave solutions for nonlinear burgers equations using the multiple exp-function method

2021 ◽  
pp. 2150149
Author(s):  
Khaled A. Gepreel ◽  
E. M. E. Zayed
Keyword(s):  
Traveling Wave ◽  
Software Package ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Multiple Wave ◽  
Wave Solutions ◽  
The One

In this paper, we use the multiple exp-function method to explicity present traveling wave solutions, double-traveling wave (DTW) solutions and triple-traveling wave solutions (TWs) which include one-soliton, double-soliton and triple-soliton solutions for nonlinear partial differential equations (NPDEs) via, the (2+1)-dimensional and (3+1)-dimensional nonlinear Burgers PDEs in mathematical physics. In this work, we build some series of straightforward and new solutions successfully with the help of a computerized symbol computational software package like Maple or Mathematica. We will make some drawings in some cases with specific values for the relevant parameters for each obtained solutions such as the one-traveling wave solutions, double-traveling wave solutions and TWs. This method is efficient and powerful in solving a wide class of NPDEs.

scholarly journals Transient Flow in Gas Networks: Traveling waves

2018 ◽  
Vol 28 (2) ◽  
pp. 341-348 ◽  
Author(s):  
Martin Gugat ◽  
David Wintergerst
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Transient Flow ◽  
Blow Up ◽  
Factor Model ◽  
Compressibility Factor ◽  
Traveling Wave Solutions ◽  
Network Nodes ◽  
Wave Solutions ◽  
The One

Abstract In the context of gas transportation, analytical solutions are helpful for the understanding of the underlying dynamics governed by a system of partial differential equations. We derive traveling wave solutions for the one-dimensional isothermal Euler equations, where an affine linear compressibility factor is used to describe the correlation between density and pressure. We show that, for this compressibility factor model, traveling wave solutions blow up in finite time. We then extend our analysis to networks under appropriate coupling conditions and derive compatibility conditions for the network nodes such that the traveling waves can travel through the nodes. Our result allows us to obtain an explicit solution for a certain optimal boundary control problem for the pipeline flow.

Bifurcations and Exact Traveling Wave Solutions of a Modified Nonlinear Schrödinger Equation

2016 ◽  
Vol 26 (06) ◽  
pp. 1650106 ◽  
Author(s):  
KitIan Kou ◽  
Jibin Li
Keyword(s):  
Dynamical Systems ◽  
Traveling Wave ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
One Dimensional ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Planar Dynamical Systems

In this paper, we consider two singular nonlinear planar dynamical systems created from the studies of one-dimensional bright and dark spatial solitons for one-dimensional beams in a nonlocal Kerr-like media. On the basis of the investigation of the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we obtain all possible explicit exact parametric representations of solutions (including solitary wave solutions, periodic wave solutions, peakon and periodic peakons, compacton solutions, etc.) under different parameter conditions.

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