Related papers: Vector NLS solitons interacting with a boundary
In a previous study (Matsuno Y, J. Phys. A: Math. Theor. 45(2012)23202), we have developed a systematic method for obtaining the bright soliton solutions of the Fokas-Lenells derivative nonlinear Schr\"odinger equation (FL equation shortly)…
We consider the following system linearly coupled by nonlinear Schr\"odinger equations in $\R^3$ $$ \left\{\begin{array}{ll} -\Delta u_j+u_j=u^3_j-\va\sum\limits_{i\neq j}^N u_i,\{1cm}& x\in \R^3, \{0.2cm}\\ u_j\in H^1(\R^3),\quad…
The Darboux transformation (DT) formulae for the derivative nonlinear Schr\"{o}dinger (DNLS) equation are expressed in concise forms, from which the multi-solitons, n-periodic solutions, higher-order hybrid-pattern solitons and some mixed…
Solitons in nonlinear optics holds a special role both in theoretical and experimental studies. Several types of evolution equations are seen to govern different situation of physical relevance. One such is the existence of both resonant…
We study the nonlinear stage of the modulation instability of a condensate in the framework of the focusing Nonlinear Schr\"{o}dinger Equation. We find a general N-solitonic solution of the focusing NLSE in the presence of a condensate by…
Based on the degenerate Darboux transformation, the $n$-order smooth positon solutions for the derivative nonlinear Schr\"{o}dinger equation are generated by means of the general determinant expression of the $N$-soliton solution, and…
We investigate the integrable structure and soliton dynamics of a coupled modified Korteweg-de Vries (cmKdV) system with a real symmetric coupling matrix. We introduce a vector reformulation of Hirota's bilinear formalism in which both the…
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…
We initiate the study of noncharacteristic boundary layers in hyperbolic-parabolic problems with Neumann boundary conditions. More generally, we study boundary layers with mixed Dirichlet--Neumann boundary conditions where the number of…
The multi-component Fokas-Lenells equation is considered. In particular, we present the multisoliton formulas for the system with plane-wave boundary conditions, as well as with mixed zero and plane-wave boundary conditions. A direct…
In this paper, a general bright-dark soliton solution in the form of Pfaffian is constructed for an integrable semi-discrete vector NLS equation via Hirota's bilinear method. One- and two-bright-dark soliton solutions are explicitly…
It is well known that the nonlinear Schr\"odinger (NLS) equation is a very important integrable equation. Ablowitz and Musslimani introduced and investigated an integrable nonlocal NLS equation through inverse scattering transform. Very…
In this work, we examine the integrable mixed coupled nonlinear Schr\"odinger (mCNLS) system, which describe the propagation of an optical pulse in a birefringent optical fiber. By the Riemann-Hilbert(RH) approach, the N-soliton solutions…
The integrable nonlocal nonlinear Schrodinger (NNLS) equation with the self-induced parity-time-symmetric potential [Phys. Rev. Lett. 110 (2013) 064105] is investigated, which is an integrable extension of the standard NLS equation. Its…
We consider a class of one dimensional Vector Nonlocal Non-linear Schr\"odinger Equation (VNNLSE) in an external complex potential with time-modulated Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the components of Schr\"odinger…
General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free…
In this work, we carry out a rigorous analysis of a multi-soliton solution of the focusing nonlinear Schr\"{o}dinger equation as the number, $N$, of solitons grows to infinity. We discover configurations of $N$-soliton solutions which…
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…
Mixed type (bright-dark) soliton solutions of the integrable N-coupled nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of focusing and defocusing type nonlinearity coefficients are obtained by using Hirota's bilinearization…
A discrete analogue of the dressing method is presented and used to derive integrable nonlinear evolution equations, including two infinite families of novel continuous and discrete coupled integrable systems of equations of nonlinear…