We establish an asymptotic stability result for Toda lattice soliton solutions, by making use of
a linearized Bäcklund transformation whose domain has codimension one. Combining a …

For Lax-pair isospectral deformations whose associated spectrum, for given initial data,
consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a …

arXiv:1701.02867v2 [nlin.SI] 11 Jan 2018 Page 1 RAREFACTION WAVES FOR THE TODA
EQUATION VIA NONLINEAR STEEPEST DESCENT IRYNA EGOROVA, JOHANNA MICHOR …

We derive the long-time asymptotics for the Toda shock problem using the nonlinear
steepest descent analysis for oscillatory Riemann--Hilbert factorization problems. We show …

We study the asymptotic behaviour of solutions of the Toda lattice Cauchy problem with step-
like initial data near the wavefront. The initial data are supposed to tend to the discrete …

We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second
order difference operators) with steplike coefficients which are asymptotically close to …

We develop direct and inverse scattering theory for Jacobi operators with a steplike quasi-
periodic finite-gap background in the same isospectral class. We derive the corresponding …

We prove the existence of non-decaying real solutions of the Johnson equation, vanishing
as x→+∞. We obtain asymptotic formulas as t→∞ for the solutions in the form of an infinite …

The scattering problem for step-like Jacobi operator Page 1 " !# '&( $&4 30 A FHG0 IED4
PRQSGT A'D6 UHG6 V XACB Y `badcf eTgihqp6prctsu#vxw e(prcty thdg ydcts s egf jlk mo%pqsrdn …

We give a survey of the long-time asymptotics for the Toda lattice with steplike constant
initial data using the nonlinear steepest descent analysis and its extension based on a …