We consider the modified Korteveg–de Vries equation on the line. The initial data are the
pure step function, ie, q (x, 0)= 0 for x≥ 0 and q (x, 0)= c for x< 0⁠, where c is an arbitrary …

Under investigation in this paper is a discrete integrable Ablowitz–Ladik equation, which has
certain applications in the electrical and optical systems. Via the Hirota method and symbolic …

We consider the modified Korteweg–de Vries equation on the line. The initial data is the
pure step function, ie q (x, 0)= cr for x⩾ 0 and q (x, 0)= cl for x< 0, where cl> cr> 0 are …

Abstract The modified Korteweg-de Vries equation on the line is considered. The initial
function is a discontinuous and piece-wise constant step function, ie $ q (x, 0)= c_r $ for $ x> …

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

Asymptotics of Rarefaction Wave Solution to the mKdV Equation Page 1 Journal of Mathematical
Physics, Analysis, Geometry 2011, vol. 7, No. 1, pp. 59–86 Asymptotics of Rarefaction Wave …

Starting from the Toda spectral problem, a mixed hierarchy of the isospectral equations and
the nonisospectral equations is constructed through discrete zero curvature equations …

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 …

Generalized matrix exponential solutions to the coupled derivative nonlinear Schrödinger
equation (DNLSE) are obtained by the inverse scattering transformation (IST). The resulting …

We investigate the spatial asymptotics of decaying solutions of the Toda hierarchy and show
that the asymptotic behaviour is preserved by the time evolution. In particular, we show that …