Search Results - "Adler, V. E."

Negative flows and non-autonomous reductions of the Volterra lattice by V. E. Adler

“…We study reductions of the Volterra lattice corresponding to stationary equations for the additional, noncommutative subalgebra of symmetries. It is shown…”
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Bogoyavlensky Lattices and Generalized Catalan Numbers by Adler, V.E.

“…We study the problem of the decay of initial data in the form of a unit step for the Bogoyavlensky lattices. In contrast to the Gurevich–Pitaevskii problem of…”
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Nonautonomous symmetries of the KdV equation and step-like solutions by Adler, V.E.

“…We study solutions of the KdV equation governed by a stationary equation for symmetries from the non-commutative subalgebra, namely, for a linear combination…”
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Matrix Painlevé II equations by Adler, V. E., Sokolov, V. V.

“…We use the Painlevé–Kovalevskaya test to find three matrix versions of the Painlevé II equation. We interpret all these equations as group-invariant reductions…”
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Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains by Adler, V. E.

“…We consider differential–difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination…”
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Integrable Möbius-invariant evolutionary lattices of second order by Adler, V. E.

“…We solve the classification problem for integrable lattices of the form u , t = f ( u −2 ,..., u 2 ) under the additional assumption of invariance with respect…”
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Non-Abelian Evolution Systems with Conservation Laws by Adler, V. E., Sokolov, V. V.

“…We find noncommutative analogs for well-known polynomial evolution systems with higher conservation laws and symmetries. The integrability of obtained…”
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Volterra Chain and Catalan Numbers by Adler, V. E., Shabat, A. B.

“…We consider the Cauchy problem for the Volterra chain with an initial condition equal to 0 in one node and 1 in the others. It is shown that this problem…”
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Some Exact Solutions of the Volterra Lattice by Adler, V. E., Shabat, A. B.

“…We study solutions of the Volterra lattice satisfying the stationary equation for its nonautonomous symmetry. We show that the dynamics in t and n are governed…”
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Cartan Matrices in the Toda–Darboux Chain Theory by Shabat, A. B., Adler, V. E.

“…We discuss a one-to-one correspondence between the polynomial first integrals of Hamiltonian systems with exponential interaction and the hyperintegrals of the…”
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Discrete nonlinear hyperbolic equations. Classification of integrable cases by Adler, V. E., Bobenko, A. I., Suris, Yu. B.

“…We consider discrete nonlinear hyperbolic equations on quad-graphs, in particular on ℤ 2 . The fields are associated with the vertices and an equation of the…”
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Classification of Integrable Equations on Quad-Graphs. The Consistency Approach by Adler, V.E., Bobenko, A.I., Suris, Yu.B.

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Negative flows and non-autonomous reductions of the Volterra lattice by Adler, V. E

“…Open Communications in Nonlinear Mathematical Physics, Special Issue in Memory of Decio Levi (February 15, 2024) ocnmp:11597 We study reductions of the…”
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Legendre transforms on a triangular lattice by Adler, V. É.

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Differential substitutions for non-Abelian equations of KdV type by Adler, V. E

“…Ufa Math. J. 13:2 (2021) 107-114 We construct non-Abelian analogs for some KdV type equations, including the (rational form of) exponential…”
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Nonautonomous symmetries of the KdV equation and step-like solutions by Adler, V. E

“…Journal of Nonlinear Mathematical Physics 27:3 (2020) 478-493 We study solutions of the KdV equation governed by a stationary equation for symmetries from the…”
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Cauchy Problem for Integrable Discrete Equations on Quad-Graphs by Adler, V. E., Veselov, A. P.

“…Initial value problems for the integrable discrete equations on quad-graphs are investigated. We give a geometric criterion of when such a problem is…”
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Model equation of the theory of solitons by Adler, V. É., Shabat, A. B.

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Integrable 7-point discrete equations and evolution lattice equations of order 2 by Adler, V. E

“…Theoretical and Mathematical Physics 195:2 (2018) 513-528 We consider differential-difference equations that determine the continuous symmetries of discrete…”
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Non-Abelian evolution systems with conservation laws by Adler, V. E, Sokolov, V. V

“…Math. Phys. Anal. Geom. 24:1 (2021) 7 We find noncommutative analogs for well-known polynomial evolution systems with higher conservation laws and symmetries…”
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