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PreprintCC BY-NC-ND 4.0HAL

Wronskian representations of the solutions to the sine-Gordon equation

  • Pierre Gaillard
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Abstract

With a specific Darboux transformation, we construct solutions to the sine-Gordon equation. We use both the simple Darboux transformation, as well as the multiple Darboux transformation which allows to obtain compact solutions of this equation. We construct explicitly some solutions for the first orders. Using particular generating functions, we give wronskian representations of the solutions to the sine-Gordon equation. In this case we give different solutions to this equation. We deduce generalized wronskian representations of the solutions to the sine-Gordon equation.

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Cite

BibTeXRIS
BibTeX
@misc{gaillard2026wronskian,
  title = {{Wronskian representations of the solutions to the sine-Gordon equation}},
  author = {Pierre Gaillard},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05763853v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Wronskian representations of the solutions to the sine-Gordon equation
AU  - Pierre Gaillard
PY  - 2026
DA  - 2026/09/25
PB  - HAL
UR  - https://hal.science/hal-05763853v1
AB  - With a specific Darboux transformation, we construct solutions to the sine-Gordon equation. We use both the simple Darboux transformation, as well as the multiple Darboux transformation which allows to obtain compact solutions of this equation. We construct explicitly some solutions for the first orders. Using particular generating functions, we give wronskian representations of the solutions to the sine-Gordon equation. In this case we give different solutions to this equation. We deduce generalized wronskian representations of the solutions to the sine-Gordon equation.
ER  -