Exactly Solvable and Integrable Systems

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New submissions for Mon, 29 Apr 24

[1]  arXiv:2404.17156 [pdf, other]

Title: Construction of a new (3 + 1)-dimensional KdV equation and its closed-form solutions with solitary wave behaviour and conserved vectors

Authors: Nardjess Benoudina, Chaudry Massood Khalique, Ji Lin

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

This paper discusses the construction of a new $(3+1)$-dimensional Korteweg-de Vries (KdV) equation. By employing the KdV's recursion operator, we extract two equations, and with elemental computation steps, the obtained result is $ 3u_{xyt}+3u_{xzt}-(u_{t}-6uu_{x}+u_{xxx})_{yz}-2\left(u_{x}\partial_{x}^{-1}u_{y}\right)_{xz}-2\left(u_{x}\partial_{x}^{-1}u_{z}\right)_{xy}=0 $. We then transform the new equation to a simpler one to avoid the appearance of the integral in the equation. Thereafter, we apply the Lie symmetry technique and gain a $7$-dimensional Lie algebra $L_7$ of point symmetries. The one-dimensional optimal system of Lie subalgebras is then computed and used in the reduction process to achieve seven exact solutions. These obtained solutions are graphically illustrated as 3D and 2D plots that show different propagations of solitary wave solutions such as breather, periodic, bell shape, and others. Finally, the conserved vectors are computed by invoking Ibragimov's method.

Replacements for Mon, 29 Apr 24

[2]  arXiv:2312.13122 (replaced) [pdf, other]

Title: Screwon spectral statistics and dispersion relation in the quantum Rajeev-Ranken model

Authors: Govind S. Krishnaswami, T. R. Vishnu

Comments: 17 pages, 21 figure files, Discussion section expanded

Journal-ref: Physica D, 463 (2024) 134170

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

[3]  arXiv:2403.16285 (replaced) [pdf, other]

Title: SKdV, SmKdV flows and their supersymmetric gauge-Miura transformations

Authors: Y.F. Adans, A.R. Aguirre, J.F. Gomes, G.V. Lobo, A.H. Zimerman

Comments: 22 pages Latex

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

[4]  arXiv:2402.02990 (replaced) [pdf, ps, other]

Title: Poisson-Lie analogues of spin Sutherland models revisited

Authors: L. Feher

Comments: 32 pages, v2: slightly modified the abstract and corrected small typos

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

• New submissions
• Replacements