scholarly journals Homotopic mapping solution of soliton for perturbed KdV equation

2008 ◽  
Vol 57 (12) ◽  
pp. 7419
Author(s):  
Mo Jia-Qi ◽  
Yao Jing-Sun
Keyword(s):  
Kdv Equation ◽  
Mapping Solution ◽  
Perturbed Kdv Equation ◽  
Homotopic Mapping

scholarly journals Solutions of the perturbed KdV equation for convecting fluids by factorizations

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Octavio Cornejo-Pérez ◽  
Haret Rosu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Kdv Equation ◽  
Travelling Wave ◽  
Second Order ◽  
Travelling Wave Solutions ◽  
Second Order Differential Equation ◽  
Wave Solutions ◽  
Perturbed Kdv Equation

AbstractIn this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential andWeierstrass functions.

scholarly journals A solitary-wave solution to a perturbed KdV equation

2000 ◽  
Vol 64 (4) ◽  
pp. 475-480 ◽  
Author(s):  
M. A. ALLEN ◽  
G. ROWLANDS
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Kdv Equation ◽  
Perturbation Expansion ◽  
Approximate Form ◽  
First Order Correction ◽  
Higher Order Corrections ◽  
Perturbed Kdv Equation ◽  
Secular Terms

We derive the approximate form and speed of a solitary-wave solution to a perturbed KdV equation. Using a conventional perturbation expansion, one can derive a first-order correction to the solitary-wave speed, but at the next order, algebraically secular terms appear, which produce divergences that render the solution unphysical. These terms must be treated by a regrouping procedure developed by us previously. In this way, higher-order corrections to the speed are obtained, along with a form of solution that is bounded in space. For this particular perturbed KdV equation, it is found that there is only one possible solitary wave that has a form similar to the unperturbed soliton solution.

LOW-DIMENSIONAL CHAOS IN A PERTURBED KORTEWEG–DE VRIES EQUATION

1995 ◽  
Vol 05 (04) ◽  
pp. 1221-1233 ◽  
Author(s):  
X. TIAN ◽  
R. H. J. GRIMSHAW
Keyword(s):  
Steady State ◽  
Vries Equation ◽  
Numerical Study ◽  
Kdv Equation ◽  
Period Doubling ◽  
Subharmonic Bifurcation ◽  
De Vries ◽  
Route To Chaos ◽  
Low Dimensional ◽  
Perturbed Kdv Equation

Spatial chaos has been observed in the steady state from a numerical study of a perturbed Korteweg–de Vries equation. The onset of chaos is due to a subharmonic bifurcation sequence. A second route to chaos is also observed via a period-doubling sequence generated from each fundamental subharmonic state. In this paper, the question of determining low-dimensional chaos in this perturbed KdV equation is addressed. The dimension of this system in the steady state is estimated from the corresponding ordinary differential equation via the Lyapunov spectrum, and also from a numerical investigation via a reconstructed attractor using a spatial series.

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