A NEW PERSPECTIVE TO STUDY THE THIRD-ORDER MODIFIED KDV EQUATION ON FRACTAL SET

Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050110 ◽  
Author(s):  
JIAN-GEN LIU ◽  
XIAO-JUN YANG ◽  
YI-YING FENG ◽  
PING CUI
Keyword(s):  
Kdv Equation ◽  
Bäcklund Transformations ◽  
Nonlinear Phenomena ◽  
Third Order ◽  
Fractal Set ◽  
The Third ◽  
Backlund Transformations ◽  
Modified Kdv Equation ◽  
Constant Coefficients ◽  
New Perspective

In this paper, we construct the Bäcklund transformations and the super-position formulas to the constant coefficients local fractional Riccati equation for the first time. Next, by means of the Bäcklund transformations and seed solutions which have been known in [X. J. Yang et al., Non-differentiable solutions for local fractional nonlinear Riccati differential equations, Fundam. Inform. 151(1–4) (2017) 409–417], we can get a class of exact solutions to the third-order modified KdV equation on the fractal set. These new type solutions can assist us to review different nonlinear phenomena better, which had been modeled via local fractional derivative.

An Numeric Method on the Third Order Term of KDV Equation

2011 ◽  
Vol 135-136 ◽  
pp. 253-255
Author(s):  
Yi Min Tian
Keyword(s):  
Difference Scheme ◽  
Kdv Equation ◽  
Order Term ◽  
Boundary Value ◽  
Difference Schemes ◽  
Boundary Values ◽  
Implicit Difference Scheme ◽  
Third Order ◽  
The Third ◽  
Numeric Experiment

Numeric scheme and numeric result was in this paper. First, We proposes a kind of explicit - implicit difference scheme to solve the initial and boundary value questions of the third order term of KDV equation here,and so we can solve the problem that the additional boundary values must be given first for present difference schemes when we try to realize the calculation by then., second, numeric experiment results was given ay the end of this article.

scholarly journals Bäcklund Transformations between the KdV Equation and a New Nonlinear Evolution Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Xifang Cao
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
The Other ◽  
Bäcklund Transformations ◽  
Backlund Transformations ◽  
The Kdv Equation ◽  
New Equation

We first give a Bäcklund transformation from the KdV equation to a new nonlinear evolution equation. We then derive two Bäcklund transformations with two pseudopotentials, one of which is from the KdV equation to the new equation and the other from the new equation to itself. As applications, by applying our Bäcklund transformations to known solutions, we construct some novel solutions to the new equation.

scholarly journals Bäcklund transformations for several cases of a type of generalized KdV equation

2004 ◽  
Vol 2004 (63) ◽  
pp. 3369-3377
Author(s):  
Paul Bracken
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
Bäcklund Transformations ◽  
Backlund Transformation ◽  
Generalized Kdv Equation ◽  
Backlund Transformations ◽  
De Vries ◽  
Derivative Term

An alternate generalized Korteweg-de Vries system is studied here. A procedure for generating solutions is given. A theorem is presented, which is subsequently applied to this equation to obtain a type of Bäcklund transformation for several specific cases of the power of the derivative term appearing in the equation. In the process, several interesting, new, ordinary, differential equations are generated and studied.

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