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PreprintCC BY 4.0arXiv

PT-invariant nonlocal variable-coefficient Fokas-Lenells equation: nonstandard Hirota bilinearization, symmetry-preserving and breaking multi-soliton solutions

  • Sagardeep Talukdar
  • Ramakrishnan R
  • Sudipta Nandy
  • Lakshmanan M
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Abstract

In this paper, we explore a variable-coefficient Fokas-Lenells system with gain/loss. Applying a nonlocal symmetry reduction, the system leads to a PT-invariant variable-coefficient Fokas-Lenells equation (vcFLE) with specific constraints on dispersion and nonlinearity coefficients. We prove the Lax integrability of the given system and construct one- and two-soliton solutions using a nonstandard Hirota bilinearization method. We show that, depending on the soliton parameters, the solutions can retain or violate the underlying symmetry. With appropriate choice of dispersion and nonlinearity, the system shows periodic-wave and soliton structures.

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Cite

BibTeXRIS
BibTeX
@misc{talukdar2026ptinvariant,
  title = {{PT-invariant nonlocal variable-coefficient Fokas-Lenells equation: nonstandard Hirota bilinearization, symmetry-preserving and breaking multi-soliton solutions}},
  author = {Sagardeep Talukdar and Ramakrishnan R and Sudipta Nandy and Lakshmanan M},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22357},
  eprint = {2609.22357},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22357},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - PT-invariant nonlocal variable-coefficient Fokas-Lenells equation: nonstandard Hirota bilinearization, symmetry-preserving and breaking multi-soliton solutions
AU  - Sagardeep Talukdar
AU  - Ramakrishnan R
AU  - Sudipta Nandy
AU  - Lakshmanan M
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.22357
UR  - https://arxiv.org/abs/2609.22357
AB  - In this paper, we explore a variable-coefficient Fokas-Lenells system with gain/loss. Applying a nonlocal symmetry reduction, the system leads to a PT-invariant variable-coefficient Fokas-Lenells equation (vcFLE) with specific constraints on dispersion and nonlinearity coefficients. We prove the Lax integrability of the given system and construct one- and two-soliton solutions using a nonstandard Hirota bilinearization method. We show that, depending on the soliton parameters, the solutions can retain or violate the underlying symmetry. With appropriate choice of dispersion and nonlinearity, the system shows periodic-wave and soliton structures.
ER  -