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PreprintCC BY 4.0arXiv

Large number of hyperbolic and periodic solutions of sine-Gordon equation with nontrivial time dependence

  • Thokala Soloman Raju
  • T. Shreecharan
  • Avinash Khare
  • Avadh Saxena
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Abstract

By using suitable ansatz which reduces the problem of obtaining exact solutions of the sine-Gordon equation with nontrivial time dependence to obtaining exact solutions of two first order symmetric ϕ4-like coupled equations in x and t, we obtain a large number of hyperbolic and periodic solutions of the sine-Gordon equation. In particular, we not only obtain the well-known two-soliton, soliton-antisoliton and the breather solutions but also obtain periodic two-soliton, periodic soliton-antisoliton as well as periodic breather solutions. Besides, we also obtain superposed real and complex (parity-time reversal or) 𝒫𝒯-invariant solutions related to the two-soliton, soliton-antisoliton and the breather solutions of the sine-Gordon equation.

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Cite

BibTeXRIS
BibTeX
@misc{raju2026large,
  title = {{Large number of hyperbolic and periodic solutions of sine-Gordon equation with nontrivial time dependence}},
  author = {Thokala Soloman Raju and T. Shreecharan and Avinash Khare and Avadh Saxena},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36891},
  eprint = {2610.36891},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36891},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Large number of hyperbolic and periodic solutions of sine-Gordon equation with nontrivial time dependence
AU  - Thokala Soloman Raju
AU  - T. Shreecharan
AU  - Avinash Khare
AU  - Avadh Saxena
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36891
UR  - https://arxiv.org/abs/2610.36891
AB  - By using suitable ansatz which reduces the problem of obtaining exact solutions of the sine-Gordon equation with nontrivial time dependence to obtaining exact solutions of two first order symmetric ϕ^4-like coupled equations in x and t, we obtain a large number of hyperbolic and periodic solutions of the sine-Gordon equation. In particular, we not only obtain the well-known two-soliton, soliton-antisoliton and the breather solutions but also obtain periodic two-soliton, periodic soliton-antisoliton as well as periodic breather solutions. Besides, we also obtain superposed real and complex (parity-time reversal or) 𝒫𝒯-invariant solutions related to the two-soliton, soliton-antisoliton and the breather solutions of the sine-Gordon equation.
ER  -