A global factorization theorem for the ZS-AKNS system.
Andrew Lenard: a mystery unraveled.
Bethe ansatz, inverse scattering transform and tropical Riemann theta function in a periodic soliton cellular automaton for .
Compatible flat metrics.
Darboux transformation for the nonstationary Schrödinger equation.
Erratum to Fourier diffraction theorem for the tensor fields
Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem.
Fourier diffraction theorem for the tensor fields
The paper is devoted to the electromagnetic inverse scattering problem for a dielectric anisotropic and magnetically isotropic media. The properties of an anisotropic medium with respect to electromagnetic waves are defined by the tensors, which give the relation between the inductions and the fields. The tensor Fourier diffraction theorem derived in the paper can be considered a useful tool for studying tensor fields in inverse problems of electromagnetic scattering. The method is based on the...
Initial boundary value problem for the mKdV equation on a finite interval
We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex -plane. This RH problem is determined by certain spectral functions which are defined in terms of the initial-boundary values at and . We show that the spectral functions satisfy an algebraic “global relation” which express the implicit relation between all boundary values in terms of spectral...
Integrability and beyond
Level set structure of an integrable cellular automaton.
Long time asymptotics of the Camassa–Holm equation on the half-line
We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation on the half-line . The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane , having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of spectral data...
Manin matrices, quantum elliptic commutative families and characteristic polynomial of elliptic Gaudin model.
-wave equations with orthogonal algebras: and reductions and soliton solutions.
On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension.
On the growth of Sobolev norms for the cubic Szegő equation
We report on a recent result establishing that trajectories of the cubic Szegő equation in Sobolev spaces with high regularity are generically unbounded, and moreover that, on solutions generated by suitable bounded subsets of initial data, every polynomial bound in time fails for high Sobolev norms. The proof relies on an instability phenomenon for a new nonlinear Fourier transform describing explicitly the solutions to the initial value problem, which is inherited from the Lax pair structure enjoyed...
Quantum curve in -oscillator model.
Real Hamiltonian forms of affine Toda models related to exceptional Lie algebras.
Reduction of infinite dimensional equations.
Solitons and large time behavior of solutions of a multidimensional integrable equation
Novikov-Veselov equation is a (2+1)-dimensional analog of the classic Korteweg-de Vries equation integrable via the inverse scattering translform for the 2-dimensional stationary Schrödinger equation. In this talk we present some recent results on existence and absence of algebraically localized solitons for the Novikov-Veselov equation as well as some results on the large time behavior of the “inverse scattering solutions” for this equation.