Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes
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DOI: 10.1007/jhep01(2018)148
Abstract: A bstractWe construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS3 algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions.The analysis… read more here.
Keywords: integrable systems; systems bms3; poisson structure; locally flat ... See more keywords
Cluster integrable systems and spin chains
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DOI: 10.1007/jhep10(2019)100
Abstract: Abstract We discuss relation between the cluster integrable systems and spin chains in the context of their correspondence with 5d supersymmetric gauge theories. It is shown that $$ {\mathfrak{gl}}_N $$ gl N XXZ-type spin chain… read more here.
Keywords: integrable systems; cluster integrable; spin; systems spin ... See more keywords
Integrable Systems with Dissipation and Two and Three Degrees of Freedom
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DOI: 10.1007/s10958-018-4070-z
Abstract: We establish the integrability for some classes of dynamic systems on the tangent bundles of two– and three-dimensional manifolds (systems with two and three degrees of freedom). The force fields possess the so-called variable dissipation… read more here.
Keywords: two three; integrable systems; degrees freedom; systems dissipation ... See more keywords
Integrable systems, symmetries, and quantization
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DOI: 10.1007/s11005-017-1018-z
Abstract: These notes are an expanded version of a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of Liouville, we explore the notion of non-degenerate singularities and… read more here.
Keywords: integrable systems; systems symmetries; symmetries quantization;
Lagrangian multiforms and dispersionless integrable systems
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DOI: 10.1007/s11005-025-02016-w
Abstract: We demonstrate that interesting examples of Lagrangian multiforms appear naturally in the theory of multidimensional dispersionless integrable systems as (a) higher-order conservation laws of linearly degenerate PDEs in 3D, and (b) in the context of… read more here.
Keywords: integrable systems; multiforms dispersionless; lagrangian multiforms; dispersionless integrable ... See more keywords
Separation of variables, Lax-integrable systems and gl(2)⊗gl(2)-valued classical r-matrices
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DOI: 10.1016/j.geomphys.2020.103733
Abstract: Abstract In the present paper we consider a problem of separation of variables for Lax-integrable hamiltonian system generated by general non-skew-symmetric g l ( 2 ) ⊗ g l ( 2 ) -valued classical r… read more here.
Keywords: valued classical; integrable systems; separation variables; variables lax ... See more keywords
Nonrelativistic strings on R × S2 and integrable systems
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DOI: 10.1016/j.nuclphysb.2020.115220
Abstract: Abstract We show that the (torsional) nonrelativistic string sigma models on R × S 2 can be mapped into deformed Rosochatius like integrable models in one dimension. We also explore the associated Hamiltonian constrained structure… read more here.
Keywords: integrable systems; strings integrable; nonrelativistic strings;
Pumping approximately integrable systems
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DOI: 10.1038/ncomms15767
Abstract: Weak perturbations can drive an interacting many-particle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been… read more here.
Keywords: state; integrable systems; spin; pumping approximately ... See more keywords
Cartan frames and algebras with links to integrable systems differential equations and surfaces
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DOI: 10.1063/1.5005816
Abstract: Moving frames and Clifford algebras will be used to illustrate an interconnected approach to the study of integrable systems, their surfaces, and methods for producing integrable partial differential equations. After a system of one-forms is… read more here.
Keywords: cartan frames; algebras links; integrable systems; links integrable ... See more keywords
Generators of rank 2 cluster algebras of affine types via linearization of seed mutations
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DOI: 10.1063/1.5053429
Abstract: From the viewpoint of integrable systems on algebraic curves, we discuss linearization of birational maps arising from the seed mutations of types $A^{(1)}_1$ and $A^{(2)}_2$, which enables us to construct the set of all cluster… read more here.
Keywords: seed; integrable systems; seed mutations; curve ... See more keywords
Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
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DOI: 10.1080/10652469.2016.1250082
Abstract: ABSTRACT In this work we characterize a high-order Toda lattice in terms of a family of matrix polynomials orthogonal with respect to a complex matrix measure. In order to study the solution of this dynamical… read more here.
Keywords: via matrix; interpretation integrable; integrable systems; systems via ... See more keywords