Related papers: Large order breathers of the nonlinear Schr\"oding…
We study the large-order asymptotics for the Kuznetsov-Ma breather of the nonlinear Schr\"{o}dinger equation in the far-field regime. With the aid of Darboux transformation, we first derive the corresponding Riemann-Hilbert representation…
We study the large order and infinite order soliton of the coupled nonlinear Schrodinger equation with the Riemann-Hilbert method. By using the Riemann-Hilbert representation for the high order Darboux dressing matrix, the large order and…
The integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We study families of such multiple-pole solitons generated by…
We analyze the large-$n$ behavior of soliton solutions of the integrable focusing nonlinear Schr\"odinger equation with associated spectral data consisting of a single pair of conjugate poles of order $2n$. Starting from the zero…
In this paper, we obtain the Nth-order rational solutions for the defocusing nonlocal nonlinear Schrodinger equation by the Darboux transformation and some limit technique. Then, via an improved asymptotic analysis method relying on the…
A study of high-order solitons in three nonlocal nonlinear Schr\"{o}dinger equations is presented, which includes the \PT-symmetric, reverse-time, and reverse-space-time nonlocal nonlinear Schr\"{o}dinger equations. General high-order…
We investigate the large-space and large-time asymptotic behavior of a soliton gas for the focusing nonlinear Schr\"odinger equation. The soliton gas is constructed as the continuum limit of pure $N$-soliton solutions as $N\to\infty$, with…
We investigate the long-time asymptotics for the focusing integrable discrete nonlinear Schr\"odinger equation. Under generic assumptions on the initial value, the solution is asymptotically a sum of 1-solitons. We find different phase…
We construct certain higher order smooth positon and breather positon solutions of an extended nonlinear Schr\"odinger equation with the cubic and quartic nonlinearity. We utilize the generalized Darboux transformation method to construct…
The long-time asymptotic behavior of solutions to the focusing nonlinear Schr\"odinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity is studied in the case of initial conditions that allow for the…
The long-time asymptotic behavior of the focusing nonlinear Schr\"odinger (NLS) equation on the line with symmetric nonzero boundary conditions at infinity is characterized by using the recently developed inverse scattering transform (IST)…
We construct the multi-breather solutions of the focusing nonlinear Schr\"odinger equation (NLSE) on the background of elliptic functions by the Darboux transformation, and express them in terms of the determinant of theta functions. The…
By using the Darboux transformation, we obtain two new types of exponential-and-rational mixed soliton solutions for the defocusing nonlocal nonlinear Schrodinger equation. We reveal that the first type of solution can display a large…
We study upper bounds and the asymptotic behavior of high order moments for solutions to a family of linear and nonlinear Schroedinger equations.
We present new solutions in terms of elementary functions of the multi-component nonlinear Schr\"odinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These…
We numerically investigate the long time dynamics of spatially periodic breather solutions of the 1-D nonlinear Schr\"odinger equation under parametric forcing of the form $f(x)=f_0 \exp(iKx)$ along with dissipation. In the absence of…
We consider the massive Thirring model and establish pointwise long-time behavior of its solutions in weighted Sobolev spaces. For soliton-free initial data we can show that the solution converges to a linear solution modulo a phase…
The rigorous asymptotic analysis for the Riemann problem of the defocusing nonlinear Schr\"{o}dinger hydrodynamics is a very interesting problem with many challenges. To date, the full analysis of this problem remains open. In this work,…
In this paper we compute the higher order long time asymptotics of the defocussing nonlinear Schr\"odinger equation using the $\overline{\partial}$-nonlinear steepest descent method. We assume initial condition in weighted Sobolev space…
In this work, the higher-order dispersive nonlinear Schr\"{o}dinger equation with non-zero boundary conditions at infinity is investigated including the simple and double zeros of the scattering coefficients. We introduce a appropriate…