Nonlinear Dynamics

, Volume 93, Issue 2, pp 733–740 | Cite as

New nonautonomous combined multi-wave solutions for (\(\varvec{2+1}\))-dimensional variable coefficients KdV equation

  • M. S. Osman
  • J. A. T. Machado
Original Paper


A variety of new types of nonautonomous combined multi-wave solutions of the (\(2+1\))-dimensional variable coefficients KdV equation is derived by means of the generalized unified method. These solutions are classified into three categories, namely multi- soliton, periodic and elliptic solutions. The physical insight of the waves is dressed for different values of the free parameters in the obtained solutions.


Generalized unified method Variable coefficients Combined multi-wave solutions (\(2+1\))-dimensional KdV equation 


Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this article.

Ethical standards

The authors state that this research complies with ethical standards and it does not involve either human participants or animals.


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Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt
  2. 2.Department of Electrical EngineeringInstitute of Engineering, Polytechnic of PortoPortoPortugal

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