Capturing nonlinear dynamical behavior of the (3+1)-dimensional Zakharov-Kuznetsov equation arising in shallow water waves by using Lie group theory
Kajal Bhati2022302582.kajal@dr.sharda.ac.inDepartment of Mathematics and Data ScienceSchool of Engineering and ScienceSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , Nidhi Sahninidhi.sahni@sharda.ac.inDepartment of Mathematics & Data ScienceSchool of Engineering & ScienceSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , Anshu Kumaranshukumar.sgi@gmail.comDepartment of Mathematics and Data ScienceSchool of Engineering and ScienceSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , *Khursheed AlamCorresponding authorkhursheed.alam@sharda.ac.inDepartment of Mathematics & Data ScienceThe A. H. Siddiqi Centre for Advanced Research in Applied Mathematics & Physics (CARAMP)Sharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile →
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- Received:
- 01 Jan 2026
- Published Online:
- 30 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2665
- Pages:
- 2737–2748
Abstract
In this research work, the Zakharov–Kuznetsov equation is solved analytically utilizing the similarity transformations approach via classical theory of Lie-group. At each stage, the similarity transformation technique (STM) lowers the number of independent variables by one. The STM is applied to Zakharov–Kuznetsov (ZK) equation and after successive application it reduces an ordinary differential equation. This can be solved further to get invariant solutions of the Zakharov–Kuznetsov equation. This research has the potential to solve Zakharov–Kuznetsov equation in a more general approach. Fluid mechanics, oceanography, optical fiber, fluid dynamics are all applications of the system.
Keywords
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References
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