Tootfinder

Automotive Radar Online Channel Imbalance Estimation via NLMS
Esmaeil Kavousi Ghafi, Oliver Lang, Matthias Wagner, Alexander Melzer, Mario Huemer
https://arxiv.org/abs/2506.10841 …

Automotive Radar Online Channel Imbalance Estimation via NLMS
Automotive radars are one of the essential enablers of advanced driver assistance systems (ADASs). Continuous monitoring of the functional safety and reliability of automotive radars is a crucial requirement to prevent accidents and increase road safety. One of the most critical aspects to monitor in this context is radar channel imbalances, as they are a key parameter regarding the reliability of the radar. These imbalances may originate from several parameter variations or hardware fatigues, …

Replaced article(s) found for nlin.SI. https://arxiv.org/list/nlin.SI/new
[1/1]:
Discrete Lagrangian multiforms for ABS equations II: tetrahedron and octahedron equations
…

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 …

Interpretable Neural Network Quantum States for Solving the Steady States of the Nonlinear Schr\"odinger Equation
Mingshu Zhao, Zhanyuan Yan
https://arxiv.org/abs/2506.10219 …

Interpretable Neural Network Quantum States for Solving the Steady States of the Nonlinear Schrödinger Equation
The nonlinear Schrödinger equation (NLSE) underpins nonlinear wave phenomena in optics, Bose-Einstein condensates, and plasma physics, but computing its excited states remains challenging due to nonlinearity-induced non-orthonormality. Traditional methods like imaginary time evolution work for ground states but fail for excited states. We propose a neural network quantum state (NNQS) approach, parameterizing wavefunctions with neural networks to directly minimize the energy functional, enablin…

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…

Replaced article(s) found for nlin.SI. https://arxiv.org/list/nlin.SI/new/
[1/1]:
Knizhnik-Zamolodchikov equations and integrable hyperbolic Landau-Zener models

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…

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 …

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.