Numerical solutions of space fractional variable-coefficient KdV-modified KdV equation by Fourier spectral method

Fractals ◽  
2021 ◽  
Author(s):  
Che Han ◽  
Yu-Lan Wang ◽  
Zhi-Yuan Li
Keyword(s):  
Spectral Method ◽  
Variable Coefficient ◽  
Numerical Solutions ◽  
Kdv Equation ◽  
Fourier Spectral Method ◽  
Modified Kdv Equation

VARIABLE-COEFFICIENT MIURA TRANSFORMATIONS AND INTEGRABLE PROPERTIES FOR A GENERALIZED VARIABLE-COEFFICIENT KORTEWEG–de VRIES EQUATION FROM BOSE–EINSTEIN CONDENSATES WITH SYMBOLIC COMPUTATION

2009 ◽  
Vol 23 (04) ◽  
pp. 571-584 ◽  
Author(s):  
JUAN LI ◽  
BO TIAN ◽  
XIANG-HUA MENG ◽  
TAO XU ◽  
CHUN-YI ZHANG ◽  
...  
Keyword(s):  
Symbolic Computation ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Kdv Equation ◽  
Nonlinear Superposition ◽  
Modified Kdv Equation ◽  
De Vries ◽  
The One ◽  
Bose Einstein ◽  
Miura Transformations

In this paper, a generalized variable-coefficient Korteweg–de Vries (KdV) equation with the dissipative and/or perturbed/external-force terms is investigated, which arises in arterial mechanics, blood vessels, Bose gases of impenetrable bosons and trapped Bose–Einstein condensates. With the computerized symbolic computation, two variable-coefficient Miura transformations are constructed from such a model to the modified KdV equation under the corresponding constraints on the coefficient functions. Meanwhile, through these two transformations, a couple of auto-Bäcklund transformations, nonlinear superposition formulas and Lax pairs are obtained with the relevant constraints. Furthermore, the one- and two-solitonic solutions of this equation are explicitly presented and the physical properties and possible applications in some fields of these solitonic structures are discussed and pointed out.

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