BÄCKLUND TRANSFORMATION AND DIVERSE EXACT EXPLICIT SOLUTIONS OF THE FRACTAL COMBINED KdV–mKdV EQUATION

Kang-Jia Wang ()
Additional contact information
Kang-Jia Wang: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 09, 1-10

Abstract: A fractal modification of the combined KdV–mKdV equation which plays a key role in various fields of physics is presented in this work for the first time. Aided by the fractal two-scale transform, the homogeneous balance method is employed to construct the fractal Bäcklund transformation. By means of the Bäcklund transformation, some new exact explicit solutions such as the algebraic solitary wave solution of rational function, single-soliton solution, double-soliton solutions, N-soliton solutions, singular traveling solutions and the periodic wave solutions of trigonometric function are obtained. Finally, some solutions are illustrated with different fractal orders in the form of the 3D plot, 3D density and 2D curves by assigning reasonable parameters with the help of Mathematica. The findings in this paper are expected to present some new insights into the fractal theory of the fractal PDEs.

Keywords: He’s Fractal Derivative; Fractal Two-Scale Transform; Homogeneous Balance Method; Fractal Bäcklund Transformation; Exact Explicit Solutions (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X22501894
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:30:y:2022:i:09:n:s0218348x22501894

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X22501894

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().