Related papers: Large-time asymptotics for the defocusing Manakov …

We derive asymptotic formulas for the solution of the derivative nonlinear Schr\"odinger equation on the half-line under the assumption that the initial and boundary values lie in the Schwartz class. The formulas clearly show the effect of…

We consider the global existence and scattering for solutions of magnetic Zakharov system in three-dimensional space. When the initial data is small, we prove the existence of smooth global solutions and scattering results, by combining the…

Perturbation approaches developed so far for the dark soliton solutions of the (fully integrable) defocusing nonlinear Schroedinger equation cannot describe the dynamics resulting from dissipative perturbations of the Ginzburg-Landau type.…

This work is devoted to systematically study general $N$-soliton solutions possibly containing multiple degenerate soliton groups (DSGs), in the context of the sharp-line Maxwell-Bloch equations with a zero background.We also show that…

Consideration in this present paper is the long-time asymptotic of solutions to the derivative nonlinear Schr$\ddot{o}$dinger equation with the step-like initial value \begin{eqnarray} q(x,0)=q_{0}(x)=\begin{cases} \begin{split}…

In this paper, we consider the Cauchy problem for the defocusing nonlinear Schr$\ddot{\text{o}}$dinger equation with a finite genus algebro-geometric background. Long-time asymptotics of the solution are derived in four space-time regions.…

In this work, we study the Cauchy problem of integrable nonlocal Lakshmanan-Porsezian-Daniel equation with rapid attenuation of initial data. The basis Riemann-Hilbert problem of integrable nonlocal Lakshmanan-Porsezian-Daniel equation is…

We investigate the Manakov model or, more generally, the vector nonlinear Schr\"odinger equation on the half-line. Using a B\"acklund transformation method, two classes of integrable boundary conditions are derived: mixed Neumann/Dirichlet…

Using the steepest descent method of Deift-Zhou, we derive locally uniform asymptotic formulas for the Meixner polynomials. These include an asymptotic formula in a neighborhood of the origin, a result which as far as we are aware has not…

We consider numerical solution of Coupled Nonlinear Schr\"{o}dinger Equation. We prove stability and convergence in the $L_2$ space for an explicit scheme which estimations is used for implicit scheme and compare both method. As a test we…

Whether the global existence and uniqueness of strong solutions of $n$-dimensional incompressible magnetohydrodynamic (MHD for short) equations with only kinematic viscosity or magnetic diffusion holds true or not remains an outstanding…

We review some recent results on the theory of scattering and more precisely on the local Cauchy problem at infinity in time for some long range nonlinear systems including some form of the Schr"odinger equation. We consider in particular…

We use the Deift-Zhou method to obtain, in the solitonless sector, the leading order asymptotic of the solution to the Cauchy problem of the Fokas-Lenells equation as $t\ra+\infty$ on the full-line.

Consider the focusing cubic semilinear Schroedinger equation in R^3 i \partial_t \psi + \Delta \psi + | \psi |^2 \psi = 0. It admits an eight-dimensional manifold of special solutions called ground state solitons. We exhibit a…

In this paper, we consider the Cauchy problem for the modified NLS equation. Using nonlinear steepest descent method and combining the Dbar-analysis, we show that inside any fixed cone, the long time asymptotic behavior of the solution for…

We construct a class of infinite-order multisoliton solutions of the Benjamin-Ono equation on the line, for which the initial data exhibits slow spatial decay. We prove that in the long-time asymptotics, such a solution decouples as an…

We show that the inverse scattering map for the linear system associated with the defocussing Davey-Stewartson II equation is locally Lipschitz continuous with locally Lipschitz continuous inverse on $H^{1,1}(R^2)$. From the inverse…

Techniques are developed for decoupling dissipative differential equations. The approach considered is based upon obtaining a sufficient gap in the time dependent linear portion of the equation that corresponds to the linear variational…

In this paper we give the asymptotic behavior of type I multiple orthogonal polynomials for a Nikishin system of order two with two disjoint intervals. We use the Riemann-Hilbert problem for multiple orthogonal polynomials and the steepest…

The large-time asymptotics of the solutions to a class of degenerate parabolic cross-diffusion systems is analyzed. The equations model the interaction of an arbitrary number of population species in a bounded domain with no-flux boundary…