Bounded solutions of KdV: uniqueness and the loss of almost periodicity
DOI10.1215/00127094-2023-0035zbMATH Open1542.35339MaRDI QIDQ6566365
Andreia Chapouto, Monica Visan, Rowan Killip
Publication date: 3 July 2024
Published in: Duke Mathematical Journal (Search for Journal in Brave)
KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Almost and pseudo-almost periodic solutions to PDEs (35B15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bounded solutions of KdV and non-periodic one-gap potentials in quantum mechanics
- Rarefaction waves of the Korteweg-de Vries equation via nonlinear steepest descent
- Numerical simulation of nonlinear dispersive quantization
- Numerical simulation of a solitonic gas in KdV and KdV-BBM equations
- Some open problems in random matrix theory and the theory of integrable systems. II
- Uniqueness of solutions of the KdV-hierarchy via Dubrovin-type flows
- Global wellposedness of KdV in \(H^{-1}(\mathbb T,\mathbb R)\)
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
- Almost periodicity in time of solutions of the KdV equation
- On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
- Primitive potentials and bounded solutions of the KdV equation
- Invariance of white noise for KdV on the line
- Rigorous asymptotics of a KdV soliton gas
- KdV is well-posed in \(H^{-1}\)
- On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data
- Dispersive Partial Differential Equations
- THE LARGE‐TIME DEVELOPMENT OF THE SOLUTION TO AN INITIAL‐VALUE PROBLEM FOR THE KORTEWEG–DE VRIES EQUATION. II. INITIAL DATA HAS A DISCONTINUOUS COMPRESSIVE STEP
- Nonuniqueness for Solutions of the Korteweg-DeVries Equation
- Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
- On the regularization mechanism for the periodic Korteweg-de Vries equation
- Solutions of the korteweg–devries equation with steplike initial profile
- Some open problems in random matrix theory and the theory of integrable systems
- The large-time development of the solution to an initial-value problem for the Korteweg–de Vries equation: I. Initial data has a discontinuous expansive step
- Dispersive Quantization
- Almost Periodic Solutions of the KdV Equation
- Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points
- The collisionless shock region for the long‐time behavior of solutions of the KdV equation
- Integer, fractional and fractal Talbot effects
- KdV hierarchy via Abelian coverings and operator identities
- Local Well-Posedness of the KdV Equation with Quasi-Periodic Initial Data
- KdV on an incoming tide
- Long-time asymptotics for the Korteweg–de Vries equation with step-like initial data
- On the evolution of a reflection coefficient under the Korteweg–de Vries flow
- Soliton gas in integrable dispersive hydrodynamics
This page was built for publication: Bounded solutions of KdV: uniqueness and the loss of almost periodicity