相关论文: Long-time asymptotics for the Hirota equation on t…

We derive a Riemann--Hilbert representation for the solution of an integrable nonlinear evolution equation with a $3 \times 3$ Lax pair. We use the derived representation to obtain formulas for the long-time asymptotics.

This paper is concerned with the initial-boundary value problem on the full Euler-Poisson system for ions over a half line. We establish the existence of stationary solutions under the Bohm criterion similar to the isentropic case and…

This paper discusses the initial-boundary-value problems (IBVP) of nonlinear Schr\"odinger equations posed in a half plane $\mathbb{R} \times \mathbb{R}^+$ with nonhomogeneous Dirichlet boundary conditions. For any given $s \ge 0$, if the…

Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global existence, uniqueness and long-time decay of weak and regular…

We prove local well-posedness for the initial-boundary-value problem associated to some quadratic nonlinear Schr\"odinger equations on the half-line. The results are obtained in the low regularity setting by introducing an analytic family…

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}…

We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…

We prove large time asymptotics for solutions of the KP I equation with small initial data. Our assumptions on the initial data rule out lump solutions but give a precise description of the radiation field at large times. Our analysis uses…

This paper investigates fractional Riesz-Bessel equations with random initial conditions. The spectra of these random initial conditions exhibit singularities both at zero frequency and at non-zero frequencies, which correspond to the cases…

In this study by applying an own technique we investigate some asymptotic approximation properties of new type discontinuous boundary-value problems, which consists of a Sturm-Liouville equation together with eigenparameter-dependent…

In this contribution we present an overview of our work on the numerical simulation of the perturbation of a black hole space-time by incoming gravitational waves. The formulation we use is based on Friedrich's general conformal equations…

We study systematically a matrix Riemann-Hilbert problem for the modified Landau-Lifshitz (mLL) equation with nonzero boundary conditions at infinity. Unlike the zero boundary conditions case, there occur double-valued functions during the…

It is studied the Hilbert boundary value problem for the nondegenerate Beltrami equations in domains $D$ of the complex plane $\mathbb C$ with the so--called quasihyperbolic boundary condition. It is proved the existence of solutions of…

We present a Riemann-Hilbert problem formalism for the initial-boundary value problem for the Sasa-Satsuma(SS) equation: $iq_T+\frac{1}{2}q_{XX}+|q|^2q+i\eps (q_{XXX}+6|q|^2q_X+3q(|q|^2)_X)=0$ on the half-line. And we also analysis the…

Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…

We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on a finite interval (0,2pi). The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous…

We consider the long-time properties of the an obstruction in the Riemann-Hilbert approach to one dimensional focusing Nonlinear Schr\"odinger equation in the semiclassical limit for a one parameter family of initial conditions. For certain…

We consider the Dirichlet problem for the focusing NLS equation on the half-line, with given Schwartz initial data and boundary data $q(0,t)$ equal to an exponentially decaying perturbation $u(t)$ of the periodic boundary data $ a…

We investigate the Cauchy problem of a new higher-order nonlinear Schr\"{o}dinger equation (NHNSE) with weighted Sobolev initial data which is derived by ourselves. By applying $\bar{\partial}$-steepest descent method, we derive the…

We consider the modified Korteveg de Vriez equation on the whole line. Initial data is real and step-like, i.e. $q(x,0)=0$ for $x\geq0$ and $q(x,0)=c$ for $x<0$, where c is arbitrary real number. The goal of this paper is to study the…