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Soliton solutions of generalized \((3+1)\)-dimensional Yu–Toda–Sasa–Fukuyama equation using Lie symmetry analysis

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Abstract

We analyze generalized \((3+1)\)-dimensional Yu–Toda–Sasa–Fukuyama(YTSF) equation, a nonlinear evolution equation to understand pulse behavior when variations are strong. Using the Lie symmetry reduction, the generalized form of (3+1)-dimensional YTSF equation is reduced to ordinary differential equations. We introduce the main result for the analysis of soliton solutions that accounts for perturbation and dispersion of the waveform including linear and nonlinear effects. We discuss soliton interactions as a key feature of soliton based telecommunication transmission systems. Solitons propagate at distinct speed and interact quite strongly with each other having beaming correspondence. Though the interaction is transient, the coherence is diagonally placed. The solitons after perfectly elastic collisions recover their shape, amplitude and velocity except phase shift.

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Funding

This work was supported by Indian Institute of Technology Delhi (Grant No. IITDHRD’M101973G AWC9216 IC7569).

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  1. Department of Management studies, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Vishakha Jadaun & Nitin Raja Singh

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  1. Vishakha Jadaun
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  2. Nitin Raja Singh
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Correspondence to Vishakha Jadaun.

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Jadaun, V., Singh, N.R. Soliton solutions of generalized \((3+1)\)-dimensional Yu–Toda–Sasa–Fukuyama equation using Lie symmetry analysis. Anal.Math.Phys. 10, 42 (2020). https://doi.org/10.1007/s13324-020-00385-0

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  • DOI: https://doi.org/10.1007/s13324-020-00385-0

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