Heun-Wronskian Analysis of the Lax Spectrum for Sine-Gordon Kink-Breather Solutions

Volkan Ala

doi:10.53570/jnt.1833273

Heun-Wronskian Analysis of the Lax Spectrum for Sine-Gordon Kink-Breather Solutions

Abstract

We study the Lax spectrum of kink-breather solutions on cnoidal backgrounds for the integrable sine-Gordon equation. Linearizing around a kink-breather configuration on a periodic (cnoidal) carrier leads to a Schrödinger-type spectral problem with an elliptic potential given by the cosine of the background field. Using a Jacobi-elliptic change of variables adapted to the cnoidal structure, we reduce this second-order equation to a Heun-type differential equation. Two linearly independent Heun solutions are then used to build a Wronskian determinant whose zeros describe the Floquet-Bloch band-gap structure of the Lax spectrum. We discuss how the spectral bands and isolated eigenvalues (internal modes) depend on the physical and background parameters, and we relate limiting regimes such as the pure cnoidal background and the solitary kink limit to classical Lame- and Pöschl-Teller-type spectral problems.

Keywords

References

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Details

Primary Language

English

Subjects

Partial Differential Equations, Dynamical Systems in Applications, Applied Mathematics (Other)

Journal Section

Research Article

Authors

Volkan Ala ^*
0000-0002-8499-9979
Türkiye

Publication Date

December 31, 2025

Submission Date

November 30, 2025

Acceptance Date

December 30, 2025

Published in Issue

Year 2025 Number: 53

DOI

https://doi.org/10.53570/jnt.1833273

IZ

https://izlik.org/JA27RR85XH

Cite

RIS / Bibtex

APA

Ala, V. (2025). Heun-Wronskian Analysis of the Lax Spectrum for Sine-Gordon Kink-Breather Solutions. Journal of New Theory, 53, 96-111. https://doi.org/10.53570/jnt.1833273

AMA

1.Ala V. Heun-Wronskian Analysis of the Lax Spectrum for Sine-Gordon Kink-Breather Solutions. JNT. 2025;(53):96-111. doi:10.53570/jnt.1833273

Chicago

Ala, Volkan. 2025. “Heun-Wronskian Analysis of the Lax Spectrum for Sine-Gordon Kink-Breather Solutions”. Journal of New Theory, nos. 53: 96-111. https://doi.org/10.53570/jnt.1833273.

EndNote

Ala V (December 1, 2025) Heun-Wronskian Analysis of the Lax Spectrum for Sine-Gordon Kink-Breather Solutions. Journal of New Theory 53 96–111.

IEEE

[1]V. Ala, “Heun-Wronskian Analysis of the Lax Spectrum for Sine-Gordon Kink-Breather Solutions”, JNT, no. 53, pp. 96–111, Dec. 2025, doi: 10.53570/jnt.1833273.

ISNAD

Ala, Volkan. “Heun-Wronskian Analysis of the Lax Spectrum for Sine-Gordon Kink-Breather Solutions”. Journal of New Theory. 53 (December 1, 2025): 96-111. https://doi.org/10.53570/jnt.1833273.

JAMA

1.Ala V. Heun-Wronskian Analysis of the Lax Spectrum for Sine-Gordon Kink-Breather Solutions. JNT. 2025;:96–111.

MLA

Ala, Volkan. “Heun-Wronskian Analysis of the Lax Spectrum for Sine-Gordon Kink-Breather Solutions”. Journal of New Theory, no. 53, Dec. 2025, pp. 96-111, doi:10.53570/jnt.1833273.

Vancouver

1.Volkan Ala. Heun-Wronskian Analysis of the Lax Spectrum for Sine-Gordon Kink-Breather Solutions. JNT. 2025 Dec. 1;(53):96-111. doi:10.53570/jnt.1833273