Tootfinder

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…

A generalised Nehari manifold method for a class of non linear Schr\"odinger systems in $\mathbb{R}^3$
Tommaso Cortopassi, Vladimir Georgiev
https://arxiv.org/abs/2402.18483 …

A generalised Nehari manifold method for a class of non linear Schrödinger systems in $\mathbb{R}^3$
We study the existence of positive solutions of a particular elliptic system in $\mathbb{R}^3$ composed of two coupled non linear stationary Schrödinger equations (NLSEs), that is $-ε^2 Δu + V(x) u= h_v(u,v), - ε^2 Δv + V(x) v=h_u (u,v)$. Under certain hypotheses on the potential $V$ and the non linearity $h$, we manage to prove that there exists a solution $(u_ε,v_ε)$ that decays exponentially with respect to local minima points of the potential and whose energy tends to concentrate aro…

This https://arxiv.org/abs/2312.16666 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An atomic Coxeter presentation
We study parabolic double cosets in a Coxeter system by decomposing them into atom(ic coset)s, a generalization of simple reflections introduced in a joint work with Elias, Libedinsky, Patimo. We define and classify braid relations between compositions of atoms and prove a Matsumoto theorem. Together with a quadratic relation, our braid relations give a presentation of nilCoxeter algebroids similar to Demazure's presentation of nilCoxeter algebras. Our consideration of reduced compositions of a…

A generalised Nehari manifold method for a class of non linear Schr\"odinger systems in $\mathbb{R}^3$
Tommaso Cortopassi, Vladimir Georgiev
https://arxiv.org/abs/2402.18483 …

A generalised Nehari manifold method for a class of non linear Schrödinger systems in $\mathbb{R}^3$
We study the existence of positive solutions of a particular elliptic system in $\mathbb{R}^3$ composed of two coupled non linear stationary Schrödinger equations (NLSEs), that is $-ε^2 Δu + V(x) u= h_v(u,v), - ε^2 Δv + V(x) v=h_u (u,v)$. Under certain hypotheses on the potential $V$ and the non linearity $h$, we manage to prove that there exists a solution $(u_ε,v_ε)$ that decays exponentially with respect to local minima points of the potential and whose energy tends to concentrate aro…