Results 21 to 30 of about 358,156 (289)
Kadomtsev–Petviashvili Hierarchy: Negative Times
Mathematics, 2021 The Kadomtsev–Petviashvili equation is known to be the leading term of a semi-infinite hierarchy of integrable equations with evolutions given by times with positive numbers. Here, we introduce new hierarchy directed to negative numbers of times.
Andrei K. Pogrebkov
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Hodge Integrals and Integrable Hierarchies [PDF]
Letters in Mathematical Physics, 2010 We show that the generating series of some Hodge integrals involving one or two partitions are tau-functions of the KP hierarchy or the 2-Toda hierarchy respectively. We also formulate a conjecture on the connection between relative invariants and integrable hierarchies. The conjecture is verified in some examples.
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Yang-Baxter maps and the discrete KP hierarchy [PDF]
, 2009 We present a systematic construction of the discrete KP hierarchy in terms of Sato–Wilson-type shift operators. Reductions of the equations in this hierarchy to 1+1-dimensional integrable lattice systems are considered, and the problems that arise with ...
Kakei, S., Willox, R., Nimmo, J.J.C.
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A Hierarchy of Integral Operators
Rocky Mountain Journal of Mathematics, 1997 Let \(m\) and \(n\) be integers with \(m+n \geq 0\), \(m^2+ n^2>0\), we define functions \(K_{m,n}\) as follows: \[ K_{m,n} (z)= (-m)! (-1)^m \bigl[(n-1)! \pi\bigr]^{-1} z^{m-1} \overline z^{n-1} \quad \text{for} \quad m\leq 0, \] \[ K_{m,n} (z)= (-n)! (-1)^n\bigl[ (m-1)!
Begehr, Heinrich, Hile, G.N.
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Integrable viscous conservation laws [PDF]
, 2015 We propose an extension of the Dubrovin-Zhang perturbative approach to the study of normal forms for non-Hamiltonian integrable scalar conservation laws. The explicit computation of the first few corrections leads to the conjecture that such normal forms
Moro, Antonio +2 more
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Duality of positive and negative integrable hierarchies via relativistically invariant fields
Journal of High Energy Physics, 2021 It is shown that the relativistic invariance plays a key role in the study of integrable systems. Using the relativistically invariant sine-Gordon equation, the Tzitzeica equation, the Toda fields and the second heavenly equation as dual relations, some ...
S. Y. Lou, X. B. Hu, Q. P. Liu
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On integrable conservation laws [PDF]
, 2014 We study normal forms of scalar integrable dispersive (non necessarily Hamiltonian) conservation laws via the Dubrovin-Zhang perturbative scheme. Our computations support the conjecture that such normal forms are parametrised by infinitely many arbitrary
Moro, Antonio +2 more
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A List of 1 + 1 Dimensional Integrable Equations and Their Properties [PDF]
, 2001 This paper contains a list of known integrable systems. It gives their recursion-, Hamiltonian-, symplectic- and cosymplectic operator, roots of their symmetries and their scaling ...
Jing Ping Wang, Wang, Jing Ping
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Representations of sl(2,?) in category O and master symmetries [PDF]
, 2015 We show that the indecomposable sl(2,?)-modules in the Bernstein-Gelfand-Gelfand category O naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the O scheme to construct master symmetries for such
J. P. Wang, Wang, Jing Ping
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A Few Integrable Couplings of Some Integrable Systems and (2+1)-Dimensional Integrable Hierarchies
Abstract and Applied Analysis, 2014 Two high-dimensional Lie algebras are presented for which four (1+1)-dimensional expanding integrable couplings of the D-AKNS hierarchy are obtained by using the Tu scheme; one of them is a united integrable coupling model of the D-AKNS hierarchy and the
Binlu Feng, Yufeng Zhang, Huanhe Dong
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