The most well-known methods for the exact analysis of boundary value problems for linear
PDEs are the methods of (a) classical transforms,(b) images, and (c) Green's function …

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 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 …

Let q (x, t) satisfy an integrable nonlinear evolution PDE on the interval 0< x< L, and let the
order of the highest x-derivative be n. For a problem to be at least linearly well-posed one …

There exists a distinctive class of physically significant evolution PDEs in one spatial
dimension which can be treated analytically. A prototypical example of this class (which is …

The stationary, axisymmetric reduction of the vacuum Einstein equations, the so-called Ernst
equation, is an integrable nonlinear PDE in two dimensions. There now exists a general …