Exactly Solvable and Integrable Systems

Authors and titles for January 2025

[1] arXiv:2501.00121 [pdf, html, other]

Title: On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude

Evans C. Boadi, Efstathios G. Charalampidis, Panayotis G. Kevrekidis, Nicholas J. Ossi, Barbara Prinari

Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

[2] arXiv:2501.00137 [pdf, html, other]

Title: Full symmetric Toda system and vector fields on the group $SO_n(\R)$

Yu.B. Chernyakov, G.I. Sharygin

Comments: 20 pages

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Dynamical Systems (math.DS)

[3] arXiv:2501.01210 [pdf, html, other]

Title: Reductions and degenerate limits of Yang-Baxter maps with $3\times 3$ Lax matrices

P. Adamopoulou, T.E. Kouloukas, G. Papamikos

Comments: Paper submitted to a special issue of Journal of Physics A on Dualities and Symmetries in Integrable Systems

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)

[4] arXiv:2501.01941 [pdf, html, other]

Title: A Modified Davey-Stewartson System of Nonlinear Dust Acoustic Waves in (3+1)-Dimensions: Lie Symmetries and Exact Solutions

Seyma Gonul, Yasin Hasanoglu, Ayse Tiryakioglu, Yasemin Calis, Cihangir Ozemir

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)

[5] arXiv:2501.02164 [pdf, html, other]

Title: Linearization, separability and Lax pairs representation of $a_4^{(2)}$ Toda lattice

Bruce Lionnel Lietap Ndi, Djagwa Dehainsala, Joseph Dongho

Comments: 10 pages, 1 figure. arXiv admin note: text overlap with arXiv:2404.13688

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Algebraic Geometry (math.AG)

[6] arXiv:2501.02912 [pdf, html, other]

Title: Exploring the depths of symmetry in the mKdV equation: physical interpretations and multi-wave solutions

Xiazhi Hao, S. Y. Lou

Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

[7] arXiv:2501.03127 [pdf, other]

Title: On certain solvable systems of 4 nonlinear Ordinary Differential Equations

Francesco Calogero

Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

[8] arXiv:2501.03481 [pdf, html, other]

Title: Breather gas and shielding for the focusing nonlinear Schr\"odinger equation with nonzero backgrounds

Weifang Weng, Guoqiang Zhang, Boris A. Malomed, Zhenya Yan

Comments: 23 pages, 1 figure

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Pattern Formation and Solitons (nlin.PS); Optics (physics.optics)

[9] arXiv:2501.03485 [pdf, html, other]

Title: On the $N_\infty$-soliton asymptotics for the modified Camassa-Holm equation with linear dispersion and vanishing boundaries

Weifang Weng, Zhenya Yan

Comments: 43 pages, 4 figures

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)

[10] arXiv:2501.03493 [pdf, html, other]

Title: On Large-Space and Long-Time Asymptotic Behaviors of Kink-Soliton Gases in the Sine-Gordon Equation

Guoqiang Zhang, Weifang Weng, Zhenya Yan

Comments: 54 pages, 11 figures

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Optics (physics.optics)

[11] arXiv:2501.04474 [pdf, html, other]

Title: Multidimensional integrable systems from contact geometry

A. Sergyeyev

Comments: 9 pages, no figures, formatting differs from the published version etc (see the text for details), in v2 some PDF formatting issues were fixed

Journal-ref: Bol. Soc. Mat. Mex. 31 (2025), art. 26

Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

[12] arXiv:2501.04673 [pdf, html, other]

Title: The Method of ${\cal M}_{n}$-Extension: The KdV Equation

Metin Gürses, Aslı Pekcan

Comments: 11 pages

Journal-ref: Phys. Lett. A 333, 130217 (2025)

Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

[13] arXiv:2501.04984 [pdf, html, other]

Title: Reduction properties of the KP-mKP hierarchy

Lumin Geng, Jianxun Hu, Chao-Zhong Wu

Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

[14] arXiv:2501.05650 [pdf, html, other]

Title: A fast algorithmic way to calculate the degree growth of birational mappings

Basil Grammaticos, Alfred Ramani, Adrian Stefan Carstea, Ralph Willox

Comments: 18 pages, 4 figures

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)

[15] arXiv:2501.06476 [pdf, html, other]

Title: The direct linearization scheme with the Lam\'e function: The KP equation and reductions

Xing Li, Ying-ying Sun, Da-jun Zhang

Comments: 25 pages

Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

[16] arXiv:2501.07862 [pdf, html, other]

Title: Reality conditions for sine-Gordon equation and quasi-periodic solutions in finite phase spaces

Julia Bernatska

Comments: 28 pages, 4 figures. arXiv admin note: text overlap with arXiv:2312.10859

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)

[17] arXiv:2501.09313 [pdf, html, other]

Title: Invariant Reduction for Partial Differential Equations. II: The General Mechanism

Kostya Druzhkov, Alexei Cheviakov

Comments: 27 pages

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Differential Geometry (math.DG)

[18] arXiv:2501.09463 [pdf, other]

Title: Some properties of the simple nonlinear recursion $y(\ell + 1) = [1-y(\ell)]^p$ with $p$ an arbitrary positive integer

Francesco Calogero

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Classical Analysis and ODEs (math.CA)

[19] arXiv:2501.00026 (cross-list from nlin.PS) [pdf, html, other]

Title: Robust Dynamics of Rogue waves, Breathers and Mixed Bound State Solutions in Spin-Orbit and Rabi Coupled Condensates

P.S.Vinayagam, R.Radha

Comments: 15 pages, 11 figures, Accepted for Publication in Physics Letters A

Journal-ref: Phys. Lett. A 531, 130169 (2025)

Subjects: Pattern Formation and Solitons (nlin.PS); Quantum Gases (cond-mat.quant-gas); Exactly Solvable and Integrable Systems (nlin.SI)

[20] arXiv:2501.01419 (cross-list from math-ph) [pdf, html, other]

Title: Riemann-Hilbert problems, Fredholm determinants, explicit combinatorial expansions, and connection formulas for the general $q$-Painlev\'e III$_3$ tau functions

Pavlo Gavrylenko

Comments: 53 pages, 4 figures

Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Dynamical Systems (math.DS); Exactly Solvable and Integrable Systems (nlin.SI)

[21] arXiv:2501.01996 (cross-list from cond-mat.stat-mech) [pdf, html, other]

Title: Exact solvability of an Ising-type model, and exact solvability of the 6-vertex, and 8-vertex, models

Pete Rigas

Comments: 14 pages

Subjects: Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Probability (math.PR); Exactly Solvable and Integrable Systems (nlin.SI)

[22] arXiv:2501.03024 (cross-list from math.RT) [pdf, html, other]

Title: Symmetries of Grothendieck rings in representation theory

David Hernandez

Comments: 16 pages, to appear in Proceedings of the 9th European Congress of Mathematics

Subjects: Representation Theory (math.RT); Quantum Algebra (math.QA); Rings and Algebras (math.RA); Exactly Solvable and Integrable Systems (nlin.SI)

[23] arXiv:2501.04092 (cross-list from cond-mat.quant-gas) [pdf, html, other]

Title: A novel BPS bound with a first order BPS system in the $2D$ Gross-Pitaevskii equation

Fabrizio Canfora, Pablo Pais

Comments: 18 pages, 4 Figures

Subjects: Quantum Gases (cond-mat.quant-gas); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Exactly Solvable and Integrable Systems (nlin.SI); Nuclear Theory (nucl-th)

[24] arXiv:2501.04509 (cross-list from gr-qc) [pdf, html, other]

Title: Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods

Eddy B. de Leon. C. Klein, D. Korotkin

Subjects: General Relativity and Quantum Cosmology (gr-qc); Exactly Solvable and Integrable Systems (nlin.SI)

[25] arXiv:2501.05753 (cross-list from math.AG) [pdf, html, other]

Title: Dubrovin duality and mirror symmetry for ADE resolutions

Andrea Brini, Jingxiang Ma, Ian A. B. Strachan

Comments: 26 pages. Ancillary files of this arXiv submission are accessible in the directory anc/ included in the source of this manuscript. The directory contains the Wolfram Language code used to verify Proposition 3.16 for the exceptional series. A Mathematica package verifying the main conjecture in IMRN 19 (2003), 1035-1051 is also included

Subjects: Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)

[26] arXiv:2501.08250 (cross-list from hep-th) [pdf, html, other]

Title: Soliton Resonances in Four Dimensional Wess-Zumino-Witten Model

Shangshuai Li, Masashi Hamanaka, Shan-Chi Huang, Da-Jun Zhang

Comments: 35 pages, 16 figures

Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)

[27] arXiv:2501.08424 (cross-list from quant-ph) [pdf, html, other]

Title: Isochronous oscillator with a singular position-dependent mass and its quantization

Aritra Ghosh, Bhabani Prasad Mandal, Bijan Bagchi

Comments: v1: Comments are welcome

Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI); Classical Physics (physics.class-ph)

[28] arXiv:2501.08437 (cross-list from nlin.CD) [pdf, html, other]

Title: Integrals and chaos in generalized H\'{e}non-Heiles Hamiltonians

G. Contopoulos, A.C. Tzemos, F. Zanias

Comments: 18 figures

Subjects: Chaotic Dynamics (nlin.CD); Exactly Solvable and Integrable Systems (nlin.SI)

[29] arXiv:2501.08777 (cross-list from math-ph) [pdf, html, other]

Title: Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equation

D. Domanevsky, A. Levin, M. Olshanetsky, A. Zotov

Comments: 31 pages

Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Exactly Solvable and Integrable Systems (nlin.SI)