Tootfinder

This https://arxiv.org/abs/2503.03758 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Classical periodic orbits in extended phase space for spherical harmonic oscillator with spin-orbit coupling
A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables derived by semiclassical approximation to the spin coherent state path integral representation. In addition to the diametric and two circular PO families with frozen spin, solutions that bridge two circular POs are found in which orbital motion is coupled to…

This https://arxiv.org/abs/2402.02204 has been replaced.
link: https://scholar.google.com/scholar?q=a

Construction of the Lax pairs for the delay Lotka-Volterra and delay Toda lattice equations and their reductions to delay Painleve equations
The delay Lotka-Volterra and delay Toda lattice equations are delay-differential extensions of the well-known soliton equations, the Lotka-Volterra and Toda lattice equations, respectively. This paper investigates integrable properties of the delay Lotka-Volterra and delay Toda lattice equations, and study the relationships to the already known delay Painleve equations. First, Backlund transformations, Lax pairs and an infinite number of conserved quantities of these delay soliton equations are…

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions
Preet Mishra, Shyam Kumar, Sapna Ratan Shah, R. K. Brojen Singh
https://arxiv.org/abs/2505.23988

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions
Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular growth and diffusion using a Richards growth function. The solutions are obtained by using two-variable Hermite Polynomials. We estimated the parameters of the Richards function by comparing the model solutions with the experimentally observed data from scratc…

On the construction of solutions of the Davey--Stewartson I equation using an open Toda chain
I. T. Habibullin, A. R. Khakimova
https://arxiv.org/abs/2505.20786

On the construction of solutions of the Davey--Stewartson I equation using an open Toda chain
An effective method for constructing explicit solutions to the Davey--Stewartson type integrable equations is discussed based on the use of a dressing chain. The application of the method is exemplified by the equation DS I, for which a new class of explicit solutions is constructed, containing freedom in two arbitrary functions. In this case the generalized Toda lattice corresponding to the simple Lie algebra $A_2$ is used as a dressing chain.

Soliton resolution for the coupled complex short pulse equation
Nan Liu, Ran Wang
https://arxiv.org/abs/2505.22210 https://arxiv.org/…

Soliton resolution for the coupled complex short pulse equation
We address the long-time asymptotics of the solution to the Cauchy problem of ccSP (coupled complex short pulse) equation on the line for decaying initial data that can support solitons. The ccSP system describes ultra-short pulse propagation in optical fibers, which is a completely integrable system and posses a $4\times4$ matrix Wadati--Konno--Ichikawa type Lax pair. Based on the $\bar{\partial}$-generalization of the Deift--Zhou steepest descent method, we obtain the long-time asymptotic app…

This https://arxiv.org/abs/2505.20572 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Conserved Quantities in the Lorenz System
The Lorenz system, a seminal model in chaos theory, is renowned for its complex dynamics and sensitive dependence on initial conditions. This work investigates conserved quantities within the standard Lorenz equations. The system exhibits phase space volume contraction, a characteristic of dissipative systems. Despite the common understanding suggesting an absence of conserved quantities in its typical chaotic parameter regimes, this study demonstrates that the Lorenz system possesses at least …

This https://arxiv.org/abs/2505.09918 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities
We describe a family of 1+1 classical integrable space-discrete models of the Landau-Lifshitz type through the usage of ansatz for $U$-$V$ (Lax) pair with spectral parameter satisfying the semi-discrete Zakharov-Shabat equation. The ansatz for $U$-$V$ pair is based on $R$-matrices satisfying the associative Yang-Baxter equation and certain additional properties. Equations of motion are obtained using a set of $R$-matrix identities. In the continuous limit we reproduce the previously known famil…

A system of 2 nonlinearly coupled ODEs which is explicitly solvable and possibly isochronous provided its coefficients are suitably restricted
Fabio Briscese, Francesco Calogero, Farrin Payandeh
https://arxiv.org/abs/2505.24370

A system of 2 nonlinearly coupled ODEs which is explicitly solvable and possibly isochronous provided its coefficients are suitably restricted
In this paper we discuss some remarkable properties of the autonomous system of 2 first-order Ordinary Differential Equations (ODEs), which equates the derivatives $\dot{x}_n(t)$ ($n = 1, 2$) of the 2 dependent variables $x_n(t)$ to the ratios of polynomials (with constant coefficients) in the 2 variables $x_n (t)$: each of the 2 (a priori different) polynomials $P_3^{(n)}(x_1, x_2)$ in the 2 numerators is of degree 3; the 2 denominators are instead given by the same polynomial $P_1(x_1, x_2)$ …

Quasi-Homogeneous Integrable Systems: Free Parameters, Kovalevskaya Exponents, and the Painlev\'e Property
Changyu Zhou, Hayato Chiba
https://arxiv.org/abs/2505.24330

Quasi-Homogeneous Integrable Systems: Free Parameters, Kovalevskaya Exponents, and the Painlevé Property
This paper investigates quasi-homogeneous integrable systems by analyzing their Laurent series solutions near movable singularities, motivated by patterns observed in Kovalevskaya exponents of four-dimensional Painlevé-type equations. We introduce a parameter space encoding the free coefficients in these expansions and study its deformation under a commuting quasi-homogeneous vector field. Within this framework, we derive lower indicial loci from the principal one and establish an arithmetic…

This https://arxiv.org/abs/2412.20122 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Multi-component Toda lattice hierarchy
We give a detailed account of the N -component Toda lattice hierarchy. This hierarchy is an extended version of the one introduced by Ueno and Takasaki. Our version contains N discrete variables rather than one. We start from the Lax formalism, deduce the bilinear relation for the wave functions from it and then, based on the latter, prove existence of the tau-function. We also show how the multi-component Toda lattice hierarchy is embedded into the universal hierarchy which is basically the mu…