相关论文: Long-time asymptotics for the Massive Thirring mod…
We consider the one-dimensional focusing nonlinear Schr\"odinger equation (NLS) with a delta potential and even initial data. The problem is equivalent to the solution of the initial/boundary problem for NLS on a half-line with Robin…
We investigate the inverse scattering problem for the massive Thirring model, focusing particularly on cases where the transmission coefficient exhibits $N$ pairs of higher-order poles. Our methodology involves transforming initial data…
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation for decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction…
An algebraic soliton of the massive Thirring model (MTM) is expressed by the simplest rational solution of the MTM with the spatial decay of $\mathcal{O}(x^{-1})$. The corresponding potential is related to a simple embedded eigenvalue in…
In this short note, we review recent results concerning the long time dynamics of large data solutions to several dispersive models. Starting with the KdV case and ending with the KP models, we review the literature and present new results…
We study the Cauchy problem for the focusing nonlinear Kundu-Eckhaus equation and construct long time asymptotic expansion of its solution in fixed space-time cone with $C(x_1,x_2,v_1,v_2)=\{(x,t)\in\Re^2:x=x_0+vt$…
In this paper we consider the long time behavior of solutions to the cubic nonlinear Schr\"odinger equation posed on the spatial domain $\mathbb{R}\times\mathbb{T}^{d}$, $1\leq d\leq4$. For sufficiently small, smooth, decaying data we prove…
We show that the cubic Dirac equation, also known as the Thirring model, scatters at infinity to a linear solution modulo a phase correction.
The soliton resolution for the Harry Dym equation is established for initial conditions in weighted Sobolev space $H^{1,1}(\mathbb{R})$. Combining the nonlinear steepest descent method and $\bar{\partial}$-derivatives condition, we obtain…
We investigate the long-time asymptotics for the solutions to the Cauchy problem of defocusing modified Kortweg-de Vries (mKdV) equation with finite density initial data. The present paper is the subsequent work of our previous paper…
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Toda lattice for decaying initial data in the soliton region. In addition, we point out how to reduce the problem in the remaining region to the…
We study various properties of the soliton solutions of the modified regularized long-wave equation. This model possesses exact one- and two-soliton solutions but no other solutions are known. We show that numerical three-soliton…
In this work, we employ the $\bar{\partial}$-steepest descent method to investigate the Cauchy problem of the nonlocal nonlinear Schr\"{o}dinger (NNLS) equation with finite density type initial conditions in weighted Sobolev space…
We consider the Cauchy problem for the defocusing Schr$\ddot{\text{o}}$dinger (NLS) equation with a nonzero background $$\begin{align} &iq_t+q_{xx}-2(|q|^2-1)q=0, \nonumber\\ &q(x,0)=q_0(x), \quad \lim_{x \to \pm \infty}q_0(x)=\pm 1.…
We use the inverse scattering transform, the auto-Backlund transformation and the steepest descent method of Deift and Zhou to obtain the asymptotic stability of the solitons in the cubic NLS (nonlinear Schrodinger) equation.
We investigate the global well-posedness and modified scattering for the one-dimensional Schr\"odinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we…
We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schr\"odinger equation by means of the Deift-Zhou nonlinear steepest descent method. The leading term is a sum of two terms that oscillate with decay…
We consider the stability of (quasi-)periodic solutions of soliton equations under short range perturbations and give a complete description of the long time asymptotics in this situation. We show that, apart from the phenomenon of the…
We consider large time asymptotics for damped nonlinear Schr\"{o}dinger equations. It is known that the nonlinear solution asymptotically behaves like a linear solution when time $t$ tends to infinity in the energy space. We prove that its…
We review recent results on global wellposedness and long-time behavior of smooth solutions to the derivative nonlinear Schr\"{o}dinger (DNLS) equation. Using the integrable character of DNLS, we show how the inverse scattering tools and…