Tootfinder

This https://arxiv.org/abs/2307.08884 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Statistics of extreme events in integrable turbulence
We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schrödinger equation (fNLSE). This is done by invoking a stochastic interpretation of the inverse scattering transform for fNLSE and analytically evaluating the kurtosis of the emerging random nonlinear wave field in terms of the spectral density of states of the corresponding soliton gas. We then apply the general result…

This https://arxiv.org/abs/2307.08884 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Statistics of extreme events in integrable turbulence
We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schrödinger equation (fNLSE). This is done by invoking a stochastic interpretation of the inverse scattering transform for fNLSE and analytically evaluating the kurtosis of the emerging random nonlinear wave field in terms of the spectral density of states of the corresponding soliton gas. We then apply the general result…

Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks
Siyuan Xing, Efstathios G. Charalampidis
https://arxiv.org/abs/2403.04883 https:…

Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks
In this paper, we apply a machine-learning approach to learn traveling solitary waves across various families of partial differential equations (PDEs). Our approach integrates a novel interpretable neural network (NN) architecture, called Separable Gaussian Neural Networks (SGNN) into the framework of Physics-Informed Neural Networks (PINNs). Unlike the traditional PINNs that treat spatial and temporal data as independent inputs, the present method leverages wave characteristics to transform da…

Semantic Information Theory in a feedback-control Kuramoto Model
Damian R Sowinski, Adam Frank, Gourab Ghoshal
https://arxiv.org/abs/2404.02221 https://

Semantic Information Theory in a feedback-control Kuramoto Model
Semantic Information Theory (SIT) offers a new approach to evaluating the information architecture of complex systems. In this study we describe the steps required to {\it operationalize} SIT via its application to dynamical problems. Our road map has four steps: (1) separating the dynamical system into agent-environment sub-systems; (2) choosing an appropriate coarse graining and quantifying correlations; (3) identifying a measure of viability; (4) implementing a scrambling protocol and measur…

Predicting positon solutions of a family of Nonlinear Schr\"{o}dinger equations through Deep Learning algorithm
K. Thulasidharan, N. Vishnu Priya, S. Monisha, M. Senthilvelan
https://arxiv.org/abs/2405.04968

Predicting positon solutions of a family of Nonlinear Schrödinger equations through Deep Learning algorithm
We consider a hierarchy of nonlinear Schrödinger equations (NLSEs) and forecast the evolution of positon solutions using a deep learning approach called Physics Informed Neural Networks (PINN). Notably, the PINN algorithm accurately predicts positon solutions not only in the standard NLSE but also in other higher order versions, including cubic, quartic and quintic NLSEs. The PINN approach also effectively handles two coupled NLSEs and two coupled Hirota equations. In addition to the above, we…

Predicting positon solutions of a family of Nonlinear Schr\"{o}dinger equations through Deep Learning algorithm
K. Thulasidharan, N. Vishnu Priya, S. Monisha, M. Senthilvelan
https://arxiv.org/abs/2405.04968

Predicting positon solutions of a family of Nonlinear Schrödinger equations through Deep Learning algorithm
We consider a hierarchy of nonlinear Schrödinger equations (NLSEs) and forecast the evolution of positon solutions using a deep learning approach called Physics Informed Neural Networks (PINN). Notably, the PINN algorithm accurately predicts positon solutions not only in the standard NLSE but also in other higher order versions, including cubic, quartic and quintic NLSEs. The PINN approach also effectively handles two coupled NLSEs and two coupled Hirota equations. In addition to the above, we…

Comment on "Non-reciprocal topological solitons in active metamaterials"
Duilio De Santis, Bernardo Spagnolo, Angelo Carollo, Davide Valenti, Claudio Guarcello
https://arxiv.org/abs/2404.04275

Comment on "Non-reciprocal topological solitons in active metamaterials"
In the recent work "Non-reciprocal topological solitons in active metamaterials" (see arXiv:2312.03544v1), for an analytical understanding of the system under consideration, the authors derive an ordinary differential equation for the sine-Gordon (anti)soliton velocity, with the perturbation theory in the adiabatic approximation, via the inverse scattering transform formalism, see Eq. (3) in their work. Here we note that the latter equation for the (anti)soliton velocity also follows from an en…

This https://arxiv.org/abs/2402.16809 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Interactions between fractional solitons in bimodal fiber cavities
We report results of systematic investigation of dynamics featured by moving two-dimensional (2D) solitons generated by the fractional nonlinear Schroedinger equation (FNLSE) with the cubic-quintic nonlinearity. The motion of solitons is a nontrivial problem, as the fractional diffraction breaks the Galilean invariance of the underlying equation. The addition of the defocusing quintic term to the focusing cubic one is necessary to stabilize the solitons against the collapse. The setting present…

This https://arxiv.org/abs/2401.08030 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Quantized plastic deformation
In engineering crystal plasticity inelastic mechanisms correspond to tensorial zero-energy valleys in the space of macroscopic strains. The flat nature of such valleys is in contradiction with the fact that plastic slips, mimicking lattice-invariant shears, are inherently discrete. A reconciliation has recently been achieved in the mesoscopic tensorial model (MTM) of crystal plasticity, which introduces periodically modulated energy valleys while also capturing in a geometrically exact way the …

This https://arxiv.org/abs/2404.02221 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Semantic Information Theory in a feedback-control Kuramoto Model
Semantic Information Theory (SIT) offers a new approach to evaluating the information architecture of complex systems. In this study we describe the steps required to {\it operationalize} SIT via its application to dynamical problems. Our road map has four steps: (1) separating the dynamical system into agent-environment sub-systems; (2) choosing an appropriate coarse graining and quantifying correlations; (3) identifying a measure of viability; (4) implementing a scrambling protocol and measur…