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Degenerate soliton solutions and their interactions in coupled Hirota equation with trivial and nontrivial background

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Abstract

We construct two kinds of degenerate soliton solutions, one on the zero background and another on the plane wave background for the coupled Hirota equation. In the case of zero background field, we derive positon solutions of various orders. We also study interaction dynamics between positon solutions through asymptotic analysis and show that the positons exhibit time dependent phase shift during collision. We also construct hybrid solutions which composed of positons and solitons and examine the interaction between higher order positon and multi-solitons in detail. From the interaction, we demonstrate that the occurrence of elastic and inelastic interaction between multi-solitons and higher order positons. Further, we construct bound states among solitons and positons for the coupled Hirota equation. In the case of plane wave background, we construct breather-positon solutions. For the coupled Hirota equation, the breather-positon solutions are being reported first time in the literature. From the breather-positon solutions, we bring out certain interesting collision dynamics between breather-positons and positons.

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Funding

SM wishes to thank MoE-RUSA 2.0 Physical Sciences, Government of India for providing a fellowship to carry out this work. NVP thanks the Department of Science and Technology (DST), India for the financial support under Women Scientist Scheme-A. The work of MS was supported by DST-SERB, Government of India, under the Grant No. CRG/2021/002428.

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Author notes

  1. S. Monisha and N. Vishnu Priya have contributed equally to this work.

Authors and Affiliations

  1. Department of Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli, Tamil Nadu, 620 024, India

    S. Monisha & M. Senthilvelan

  2. Department of Mathematics, Indian Institute of Science, Bengaluru, Karnataka, 560 012, India

    N. Vishnu Priya

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  1. S. Monisha
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  2. N. Vishnu Priya
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  3. M. Senthilvelan
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All the authors have contributed equally to the research and to the writing up of the paper.

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Correspondence to M. Senthilvelan.

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Monisha, S., Priya, N.V. & Senthilvelan, M. Degenerate soliton solutions and their interactions in coupled Hirota equation with trivial and nontrivial background. Nonlinear Dyn 111, 21877–21894 (2023). https://doi.org/10.1007/s11071-023-08976-9

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