The Gerdjikov-Ivanov (GI) type of derivative nonlinear Schrödinger equation is considered
on the quarter plane whose initial data vanish at infinity while boundary data are time …

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 1 aims to
describe the recent progress in nonlinear differential equations and nonlinear dynamical …

We study long-time asymptotics of the solution to the Cauchy problem for the Gerdjikov-
Ivanov type derivative nonlinear Schrödinger equation iqt+ q xx− iq 2 q ̄ x+ 1 2| q| 4 q= 0 …

We consider the focusing nonlinear Schrödinger equation on the quarter plane. The initial
data are vanishing at infinity while the boundary data are time-periodic, of the form a\rm e^\i …

In this review I summarize some of the most significant advances of the last decade in the
analysis and solution of boundary value problems for integrable partial differential equations …

We consider the initial value problem for the focusing nonlinear Schrödinger equation with
“step-like” initial data: q (x, 0)= 0 for x≤ 0 and q (x, 0)= Aexp (− 2iBx) for x> 0, where A> 0 …

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 …

We consider the rigorous derivation of asymptotic formulas for initial-boundary value
problems using the nonlinear steepest descent method. We give detailed derivations of the …

In this work, we investigate a generalized nonlinear Schrödinger equation on the quarter
plane. The initial data are vanishing at infinity while the boundary data are time-periodic, of …

We consider the nonlinear Schrödinger equation on the half-line with a given Dirichlet
(Neumann) boundary datum which for large t tends to the periodic function g 0 b (t)(g 1 b (t)) …