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Exploring lump soliton solutions and wave interactions using new Inverse \((G'/G)\)-expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

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Abstract

In this research article, we propose a novel approach called the “ new Inverse \((G'/G)\)-Expansion Method” to discover new exact soliton solutions for the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain (HFSC) equation. By employing the proposed method, we successfully derive various set of new exact soliton solutions for the HFSC equation. These soliton solutions of the HFSC equation find valuable applications in various fields, including optical fiber communications, plasma physics, condensed matter physics, and nonlinear dynamics. To gain a visual understanding and illustrate the nature of the derived soliton solutions, we present 3-dimensional plots, contour plots, and 2-dimensional plots. Through these visualizations, we comprehensively observe and analyze various structures, including lump solitons, interactions of lumps with waves, periodic solitons, breather-type solitons, and solitary waves. To establish a connection between the depicted graphics and real-world phenomena, we incorporate images of transverse waves in a rope, waves on the ocean’s surface, the oscillations within the ocean depths, and bubbly waves in the application section. These real-world examples help us to bridge the gap between theoretical soliton behavior and physical occurrences, providing a deeper insight into the significance and applicability of our findings. These results significantly enhance our understanding of the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation, and also demonstrate the effectiveness of the novel Inverse \((G'/G)\)-expansion method in extracting exact soliton solutions under specific constraint conditions.

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Acknowledgements

The authors would like to express their appreciation to the Editor and the referees for their insightful and informative comments. The author, Sachin Kumar, wishes to acknowledge the Institution of Eminence, University of Delhi, India, for financial support in carrying out this research through the Faculty Research Programme Grant-IoE via Ref. No./IoE/2023-24/12/FRP.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, 110007, India

    Sachin Kumar

  2. Department of Mathematics, Shyama Prasad Mukherji College for Women, University of Delhi, Delhi, 110026, India

    Monika Niwas

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  1. Sachin Kumar
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  2. Monika Niwas
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Correspondence to Monika Niwas.

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Kumar, S., Niwas, M. Exploring lump soliton solutions and wave interactions using new Inverse \((G'/G)\)-expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation. Nonlinear Dyn 111, 20257–20273 (2023). https://doi.org/10.1007/s11071-023-08937-2

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