Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum many-body physics. We develop general approach to constructing gauge-invariant or anyonic-symmetric autoregressive neural networks, including wide range of architectures transformer recurrent network, for lattice models. These networks can be efficiently sampled explicitly obey symmetries constraint. prove that our methods provide exact representation the ground excited states two- three-dimensional toric...

We show that periodic traveling waves with sufficiently small amplitudes of the Whitham equation, which incorporates dispersion relation surface water and nonlinearity shallow equations, are spectrally unstable to long‐wavelengths perturbations if wave number is greater than a critical value, bearing out Benjamin–Feir instability Stokes waves; they stable square integrable otherwise. The proof involves spectral perturbation associated linearized operator respect Floquet exponent...

This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at forefront current research. These areas include: variational characterizations traveling waves; analytical and numerical studies periodic critical layers may overhang; existence, nonexistence, qualitative solitary fronts; localized vorticity or density stratification; in three dimensions.

Strichartz-type estimates for one-dimensional surface water-waves under tension are studied, based on the formulation of problem as a nonlinear dispersive equation. We establish family dispersion time scales depending size frequencies. infer that solution u equation we introduce satisfies local-in-time Strichartz with loss in derivative: where C depends T and norms H s -norm initial data. The proof uses frequency analysis semiclassical linealized water-wave operator.

We study the stability and instability of periodic traveling waves for Korteweg--de Vries-type equations with fractional dispersion related, nonlinear dispersive equations. show that a local constrained minimizer suitable variational problem is nonlinearly stable to period preserving perturbations, provided associated linearized operator enjoys Jordan block structure. then discuss when equation admits solutions exponentially growing in time.

Abstract We propose a shallow water model that combines the dispersion relation of waves and Boussinesq equations, extends Whitham equation to permit bidirectional propagation. show its sufficiently small periodic traveling wave is spectrally unstable long wavelength perturbations if number greater than critical value, like Benjamin‐Feir instability Stokes wave. verify associated linear operator possesses infinitely many collisions purely imaginary eigenvalues, but they do not contribute...

Abstract Periodic traveling waves are numerically computed in a constant vorticity flow subject to the force of gravity. The Stokes wave problem is formulated via conformal mapping as nonlinear pseudodifferential equation, involving periodic Hilbert transform for strip, and solved by Newton‐GMRES method. For strong positive vorticity, finite or infinite depth, overhanging profiles found amplitude increases tend touching wave, whose surface contacts itself at trough line, enclosing an air...

The classical deep-water wave problem is to find a periodic traveling with free surface of infinite depth. main result the construction global connected set rotational solutions for general class vorticities. Each nontrivial solution on continuum has profile symmetric around crests and monotone between crest trough. formulated as nonlinear elliptic boundary value in an unbounded domain parameter. analysis based generalized degree theory bifurcation. unboundedness renders consideration...

The symmetry and monotonicity properties of steady periodic gravity water waves are established for arbitrary vorticities if the wave profile is monotone near trough every streamline attains a minimum below trough. proof uses method moving planes.

A Burgers equation with fractional dispersion is proposed to model waves on the moving surfaceof a two-dimensional, infinitely deep water under influence of gravity.For certain class initial data, solution shown blow up in finite time.

The Stokes wave problem in a constant vorticity flow is formulated, by virtue of conformal mapping techniques, as nonlinear pseudodifferential equation, involving the periodic Hilbert transform, which becomes Babenko equation irrotational setting. associated linearized operator self-adjoint, whereby modified efficiently solved Newton-conjugate gradient method. For strong positive vorticity, ‘fold’ appears speed versus amplitude plane, and ‘gap’ strength increases, bounded two touching waves,...

Symmetry and monotonicity properties of solitary water-waves positive elevation with supercritical values parameter are established for an arbitrary vorticity.The proof uses the detailed knowledge asymptotic decay waves at infinity method moving planes.

We study the modulational instability of periodic traveling waves for a class Hamiltonian systems in one spatial dimension. examine how Jordan block structure associated linearized operator bifurcates small values Floquet exponent to derive criterion governing long wavelengths perturbations terms kinetic and potential energies, momentum, mass underlying wave, their derivatives. The dispersion equation is allowed be nonlocal, which Evans function techniques may not applicable. illustrate...

Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum many-body physics. We develop general approach to constructing invariant or symmetric autoregressive neural network states, including wide range of architectures Transformer recurrent (RNN), for lattice models. These networks can be efficiently sampled explicitly obey symmetries constraint. prove that our methods provide exact representation the ground excited states 2D 3D toric codes, X-cube fracton...

Journal Article Analyticity of Rotational Flows Beneath Solitary Water Waves Get access Vera Mikyoung Hur Department Mathematics, University Illinois at Urbana-Champaign, Urbana, IL 61801, USA Correspondence to be sent to: e-mail: verahur@math.uiuc.edu Search for other works by this author on: Oxford Academic Google Scholar International Mathematics Research Notices, Volume 2012, Issue 11, Pages 2550–2570, https://doi.org/10.1093/imrn/rnr123 Published: 01 January 2012 history Received: 17...

We show wave breaking---bounded solutions with unbounded derivatives---in the nonlinear nonlocal equations which combine dispersion relation of water waves and shallow extend Whitham equation to permit bidirectional propagation, provided that slope initial data is sufficiently negative.