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Study of Solitons using Efficient Technique Involving Lie Group Theory

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Abstract

This article deals with closed form solutions associated with Zoomeron equation (ZME) in \((2+1)\)-dimensions. These solutions are obtained by similarity transformations method involving Lie group theory. The symmetry reduction of ZME for different vector fields are deduced from the invariant condition of the primary equation. Next, the group invariant solutions in their explicit form are derived with the help of corresponding symmetry reductions. Initially, the partial differential equation (PDE) that consists of lesser independent variables than the primary ZME are obtained. And then, the obtained PDE is changed to new ordinary differential equation (ODE) using similarity transformations and this ODE gives the closed form of solutions for the considered ZME by back substitution. The final outcomes display that the involved methodology is quite reliable, productive and easy to solve these kinds of equations in mechanical sciences, nonlinear optics and mathematical physics.

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Authors and Affiliations

  1. Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Gandhinagar, 382007, India

    Vishakha Jadaun

  2. Department of Mathematics, Harcourt Butler Technical University, Kanpur, 208002, India

    Abhinava Srivastav

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  1. Vishakha Jadaun
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  2. Abhinava Srivastav
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Contributions

V.J. did the mathematical analysis and supervision. A.S. wrote the manuscript and prepared the figures. All authors reviewed the manuscript.

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Correspondence to Abhinava Srivastav.

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Jadaun, V., Srivastav, A. Study of Solitons using Efficient Technique Involving Lie Group Theory. Int. J. Appl. Comput. Math 10, 100 (2024). https://doi.org/10.1007/s40819-024-01736-2

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  • DOI: https://doi.org/10.1007/s40819-024-01736-2

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