Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach
From MaRDI portal
Publication:842432
DOI10.1007/s00220-008-0680-5zbMath1173.35654arXiv0801.2326OpenAlexW2039188392MaRDI QIDQ842432
Publication date: 25 September 2009
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0801.2326
KdV equations (Korteweg-de Vries equations) (35Q53) Asymptotic expansions of solutions to PDEs (35C20) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)
Related Items
On the asymptotic stability of \(N\)-soliton solutions of the defocusing nonlinear Schrödinger equation, THE RIEMANN–HILBERT APPROACH TO OBTAIN CRITICAL ASYMPTOTICS FOR HAMILTONIAN PERTURBATIONS OF HYPERBOLIC AND ELLIPTIC SYSTEMS, Complex singularities in KdV solutions, On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation, Semiclassical limit for generalized KdV equations before the gradient catastrophe, On the evolution of scattering data under perturbations of the Toda lattice, Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation, A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions, Lax Eigenvalues in the Zero-Dispersion Limit for the Benjamin–Ono Equation on the Torus, Linearizable Abel equations and the Gurevich–Pitaevskii problem, Zero-dispersion limit for the Benjamin-Ono equation on the torus with bell shaped initial data, On the critical behavior in nonlinear evolutionary PDEs with small viscosity, Numerical study of break-up in solutions to the dispersionless Kadomtsev-Petviashvili equation, Modulated equations of Hamiltonian PDEs and dispersive shocks, On parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems, Universality for the Focusing Nonlinear Schrödinger Equation at the Gradient Catastrophe Point: Rational Breathers and Poles of the Tritronquée Solution to Painlevé I, On the generation of dispersive shock waves, On critical behaviour in generalized Kadomtsev-Petviashvili equations, The scattering transform for the Benjamin-Ono equation in the small-dispersion limit, On tronquée solutions of the first Painlevé hierarchy, Semiclassical soliton ensembles for the three-wave resonant interaction equations, Rigorous asymptotics of a KdV soliton gas, On the zero-dispersion limit of the benjamin-ono cauchy problem for positive initial data, Painlevé IV Asymptotics for Orthogonal Polynomials with Respect to a Modified Laguerre Weight, Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg—de Vries equation in the small‐dispersion limit, On an isomonodromy deformation equation without the Painlevé property, On critical behaviour in systems of Hamiltonian partial differential equations, On the tritronquée solutions of \(\mathrm{P}_{\mathrm{I}}^2\), Critical behavior for scalar nonlinear waves
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Geometry of the string equations
- On deformation of Poisson manifolds of hydrodynamic type
- On Hamiltonian perturbations of hyperbolic systems of conservation laws. II: Universality of critical behaviour
- Weakly nonlinear solutions of equation \(P^ 2_ 1\)
- Inverse-scattering problem for a system of differential equations
- Semiclassical representation of the scattering matrix by a Feynman integral
- A Darboux theorem for Hamiltonian operators in the formal calculus of variations.
- Deformations of bi-Hamiltonian structures of hydrodynamic type
- Semiclassical study of quantum scattering on the line
- A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
- Universality of a double scaling limit near singular edge points in random matrix models
- On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation
- The small dispersion limit of the Korteweg-de Vries equation. I
- The korteweg-de vries equation with small dispersion: Higher order lax-levermore theory
- Korteweg‐devries equation and generalizations. VI. methods for exact solution
- On the distribution of the length of the longest increasing subsequence of random permutations
- An extension of the steepest descent method for Riemann-Hilbert problems: The small dispersion limit of the Korteweg-de Vries (KdV) equation
- Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
- The existence of a real pole-free solution of the fourth order analogue of the Painlevé I equation
- Numerical solution of the small dispersion limit of Korteweg—de Vries and Whitham equations
- Integrals of nonlinear equations of evolution and solitary waves
- The existence of unbounded solutions of the korteweg‐de vries equation
