Tootfinder

Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies
Marianna Euler, Norbert Euler
https://arxiv.org/abs/2506.07780

Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies
The term multipotentialisation of evolution equations in $1+1$ dimensions refers to the process of potentialising a given evolution equation, followed by at least one further potentialisation of the resulting potential equation. For certain equations this process can be applied several times to result in a finite chain of potential equations, where each equation in the chain is a potential equation of the previous equation. By a potentialisation of an equation with dependent variable $u$ to an …

GBDT with nontrivial seeds: explicit solutions of the focusing NLS equations and the corresponding Weyl functions
Alexander Sakhnovich
https://arxiv.org/abs/2506.07702

GBDT with nontrivial seeds: explicit solutions of the focusing NLS equations and the corresponding Weyl functions
Our GBDT (generalised Bäcklund-Darboux transformation) approach is used to construct explicit solutions of the focusing nonlinear Schrödinger (NLS) equation in the case of the exponential seed $a \exp\{2 i (cx +dt)\}$. The corresponding Baker-Akhiezer functions and evolution of the Weyl functions are obtained as well. In particular, the solutions, which appear in the study of rogue waves, step-like solutions and $N$-modulation solutions of the NLS equation are considered. This work is an esse…

Revisiting B\"acklund-Darboux transformations for KP and BKP integrable hierarchies
A. Zabrodin
https://arxiv.org/abs/2506.07208 https://

Revisiting Bäcklund-Darboux transformations for KP and BKP integrable hierarchies
We consider Bäcklund-Darboux transformations for integrable hierarchies of nonlinear equations such as KP, BKP and their close relatives referred to as modified KP and Schwarzian KP. We work in the framework of the bilinear formalism based on the bilinear equations for the tau-function. This approach allows one to extend the theory to fully difference (or discrete) versions of the integrable equations and their hierarchies in a natural way. We also show how to construct the Bäcklund-Darboux t…

Stochastic Gradient-Descent Calibration of Pyragas Delayed-Feedback Control for Chaos Suppression in the Sprott Circuit
Adib Kabir, Onil Morshed, Oishi Kabir
https://arxiv.org/abs/2506.06639

Stochastic Gradient-Descent Calibration of Pyragas Delayed-Feedback Control for Chaos Suppression in the Sprott Circuit
This paper investigates chaos control in the Sprott circuit, a minimal electronic system exhibiting complex nonlinear dynamics. Using the third-order nonlinear differential equation from Kaveh Merat paper, we model the circuit and implement delayed feedback control to suppress chaos. Experimental voltage data were extracted from published figures via WebPlotDigitizer. Then we explore two calibration techniques: Minimizing sum of squared errors (SSE), and stochastic gradient descent (SGD) with f…

The symbolic partition with generalized Koopman analysis
Haipeng Li, Pengfei Guo, Yueheng Lan
https://arxiv.org/abs/2506.06973 https://

The symbolic partition with generalized Koopman analysis
Symbolic dynamics serves as a crucial tool in the study of chaotic systems, prompting extensive research into various methods for symbolic partitioning. The limitations of these methods are heuristic and empirical for the partition the multivariate chaotic state space. Notably, the use of operator theory in partitioning the multivariable chaotic series into precise symbolic cells has been underexplored. In this paper, we propose a novel symbolic partition method, referred to as Koopman Analysis…

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…

Integrable deformations of cluster maps of type $D_{2N}$
Wookyung Kim
https://arxiv.org/abs/2506.06182 https://arxiv.org/pdf/2506.061…

Integrable deformations of cluster maps of type $D_{2N}$
In this paper, we extend one of the main results in \cite{hkm24}, of a deformed type $D_{4}$ map, to the general case of the type $D_{2N}$ for $N\geq3$. This can be achieved through a "local expansion" operation, introduced in the joint work \cite{grab} with Grabowski and Hone. This operation involves inserting a specific subquiver into the quiver arising from the Laurentification of the deformed type $D_{4}$ map. This insertion yields a new quiver, obtained through the Laurentification of the …

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…

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.