Soliton Equations and Hamiltonian Systems

By L. Dickey. 2003

805 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/774c477df223d142eb2e2dcceae3c35708564cf8

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Citations in the corpus

The Stability Analysis of the Periodic Traveling Wave Solutions of the mKdV Equation (2011, neutral): “) [36].”
Geometry of jet spaces and integrable systems (2010, background): “The literature on the Hamiltonian theory of PDEs is vast and we confine ourselves here to the key references [35, 25, 28, 30], but one feature is common to all research: theories and techniques are applicable to evolution equations only.”
Soliton Solutions of the KP Equation and Application to Shallow Water Waves (2009, methodology): “The KP equation is a completely integrable system with remarkably rich mathematical structure which is well documented in several monographs (see for examples, [1, 2, 7, 13, 19, 23, 24, 27]).”
Well-posedness and scattering for the KP-II equation in a critical space (2007, background): “There are many explicit formulas for solutions, see [4].”
Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups (2004, background): “Together these two structures form a Poisson pair, see [51, 49].”
Covariant theory of asymptotic symmetries, conservation laws and central charges (2001, methodology): “c cohomology and generalized symmetries Algebraic and diﬀerential-geometric techniques have been used for quite some time for the symmetry analysis of standard partial diﬀerential equations (see e.g. [2, 42, 40, 44] and references therein). The application of these techniques in the context of gauge”
Minimal model holography (2012, background): “♯ Actually, one can argue on general grounds [29] that, at least formally, the asymptotic symmetry algebra is the Drinfel’d-Sokolov reduction [50] (see [47] for a review) of the affine algebra based on hs[μ].”
On Hamiltonian Perturbations of Hyperbolic Systems of Conservation Laws, II: Universality of Critical Behaviour (2005, background): “subsequent considerations is the following statement (see, e.g., [ 7 ]): for two commuting Hamiltonians”
KP solitons and total positivity for the Grassmannian (2011, background): “the excedances (1, 2, 4, 7) and the soliton index [1, 7], [2, 4], [4, 9], [7, 8] in the top figure.”
Surface charge algebra in gauge theories and thermodynamic integrability (2007, background): “ its adjoint is deﬁned by Z + = (−∂) (ν)[Z (ν)·] and its ‘components’ are denoted by Z+(µ), i.e., Z+ = Z+(µ)∂ (µ). More details on the variational bicomplex can be found for instance in the textbooks [39, 41, 50, 51]. A.2 Higher order Lie-Euler operators Except for a different notation, we follow in”
Poisson vertex algebras in the theory of Hamiltonian equations (2009, neutral): “[D], [Di]).”
Weyl-Titchmarsh M-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators (2001, neutral): “, [7], [18], [27], [28], [29], [90], [94], [108], [111], [110], [112], and the references therein), especially, hierarchies of matrix-valued (i.”