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Relevant bibliographies by topics / Hydrodynamic integrable systems

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Journal articles

Academic literature on the topic 'Hydrodynamic integrable systems'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Hydrodynamic integrable systems"

1

Kupershmidt, Boris A. "Noncommutative Integrable Systems of Hydrodynamic Type." Acta Applicandae Mathematicae 92, no. 3 (2006): 269–92. http://dx.doi.org/10.1007/s10440-006-9054-1.

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2

Fava, Michele, Sounak Biswas, Sarang Gopalakrishnan, Romain Vasseur, and S. A. Parameswaran. "Hydrodynamic nonlinear response of interacting integrable systems." Proceedings of the National Academy of Sciences 118, no. 37 (2021): e2106945118. http://dx.doi.org/10.1073/pnas.2106945118.

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We develop a formalism for computing the nonlinear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb–Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.

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3

Prykarpatskyy, Yarema. "On the Integrable Chaplygin Type Hydrodynamic Systems and Their Geometric Structure." Symmetry 12, no. 5 (2020): 697. http://dx.doi.org/10.3390/sym12050697.

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A class of spatially one-dimensional completely integrable Chaplygin hydrodynamic systems was studied within framework of Lie-algebraic approach. The Chaplygin hydrodynamic systems were considered as differential systems on the torus. It has been shown that the geometric structure of the systems under analysis has strong relationship with diffeomorphism group orbits on them. It has allowed to find a new infinite hierarchy of integrable Chaplygin like hydrodynamic systems.

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4

Mokhov, O. I. "Integrable bi-Hamiltonian systems of hydrodynamic type." Russian Mathematical Surveys 57, no. 1 (2002): 153–54. http://dx.doi.org/10.1070/rm2002v057n01abeh000483.

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5

Ferapontov, E. V., and A. P. Fordy. "Separable Hamiltonians and integrable systems of hydrodynamic type." Journal of Geometry and Physics 21, no. 2 (1997): 169–82. http://dx.doi.org/10.1016/s0393-0440(96)00013-7.

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6

Odesskii, A. V., and V. V. Sokolov. "Integrable (2+1)-dimensional systems of hydrodynamic type." Theoretical and Mathematical Physics 163, no. 2 (2010): 549–86. http://dx.doi.org/10.1007/s11232-010-0043-1.

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7

Kodama, Y., and B. G. Konopelchenko. "Confluence of hypergeometric functions and integrable hydrodynamic-type systems." Theoretical and Mathematical Physics 188, no. 3 (2016): 1334–57. http://dx.doi.org/10.1134/s0040577916090051.

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8

Dubrovin, B. A. "Differential geometry of strongly integrable systems of hydrodynamic type." Functional Analysis and Its Applications 24, no. 4 (1991): 280–85. http://dx.doi.org/10.1007/bf01077332.

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9

El, Gennady A. "Soliton gas in integrable dispersive hydrodynamics." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 11 (2021): 114001. http://dx.doi.org/10.1088/1742-5468/ac0f6d.

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Abstract We review the spectral theory of soliton gases in integrable dispersive hydrodynamic systems. We first present a phenomenological approach based on the consideration of phase shifts in pairwise soliton collisions and leading to the kinetic equation for a non-equilibrium soliton gas. Then, a more detailed theory is presented in which soliton gas dynamics are modelled by a thermodynamic type limit of modulated finite-gap spectral solutions of the Korteweg–de Vries and the focusing nonlinear Schrödinger (NLS) equations. For the focusing NLS equation the notions of soliton condensate and breather gas are introduced that are related to the phenomena of spontaneous modulational instability and the rogue wave formation. The integrability properties of the kinetic equation for soliton gas are discussed and some physically relevant solutions are presented and compared with direct numerical simulations of dispersive hydrodynamic systems.

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10

De Nardis, Jacopo, Benjamin Doyon, Marko Medenjak, and Miłosz Panfil. "Correlation functions and transport coefficients in generalised hydrodynamics." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 1 (2022): 014002. http://dx.doi.org/10.1088/1742-5468/ac3658.

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Abstract We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well as linear and nonlinear response on top of equilibrium and non-equilibrium states. We consider the problems from the complementary perspectives of the general hydrodynamic theory of many-body systems, including hydrodynamic projections, and form-factor expansions in integrable models, and show how they provide a comprehensive and consistent set of exact methods to extract large scale behaviours. Finally, we overview various applications in integrable spin chains and field theories.

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