A trace formula and classical solutions to the KdV equation

DOI10.1007/978-3-031-31139-0_25MaRDI QIDQ6630042

Alexei Rybkin

Publication date: 30 October 2024

zbMATH Keywords

KdV equationtrace formula

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Applications of operator theory in the physical sciences (47N50) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Schrödinger operator, Schrödinger equation (35J10) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Meromorphic functions of one complex variable (general theory) (30D30) Canonical models for contractions and nonselfadjoint linear operators (47A45) Linear operators on spaces with an indefinite metric (47B50) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12) Elliptic operators and their generalizations (47F10) Nonselfadjoint operators (47B28)

Cites Work

• Title not available (Why is that?)
• Schrödinger operators with many bound states
• Dense point spectra of Schrödinger and Dirac operators
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• KdV is well-posed in \(H^{-1}\)
• Asymptotic approximations of integrals
• Meromorphic solutions to the KdV equation with non-decaying initial data supported on a left half line
• Solutions to the Korteweg–de Vries Equation with Initial Profile in $L_1^1 (\mathbb{R}) \cap L_N^1 (\mathbb{R}^ + )$
• Inverse scattering on the line
• Method for Solving the Korteweg-deVries Equation
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• On classical solutions of the KdV equation
• Soliton Theory and Hankel Operators

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