Related papers: Optical solitons in higher order nonlinear Schrodi…
This is the second part of a series of papers where we develop rigorous decay estimates for breather solutions of an averaged version of the non-linear Schr\"odinger equation. In this part we study the diffraction managed discrete…
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 investigate exact travelling wave solutions of higher order nonlinear Schrodinger equation in the absence of third order dispersion, which exhibit non-trivial self phase modulation. It is shown that, the corresponding dynamical equation,…
In this work, inverse scattering transform for the sixth-order nonlinear Schr\"{o}dinger equation with both zero and nonzero boundary conditions at infinity is given, respectively. For the case of zero nonzero boundary conditions, in terms…
We give an infinite number of exact solutions to the 5-dimensional static Einstein equation with axial symmetry by using the inverse scattering method. The solutions are characterized by two integers representing the soliton numbers. The…
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…
The behaviour of solitons in integrable theories is strongly constrained by the integrability of the theory; i.e. by the existence of an infinite number of conserved quantities which these theories are known to possess. One usually expects…
We consider the vector generalization of the modified Korteweg-de Vries equation. We develop the inverse scattering transform for solving this equation. We construct the solitons and the breather solutions and investigate the processes of…
The extended nonlinear Schr\"{o}dinger (ENLS) equation with third-order term and fourth-order term which describes the wave propagation in the optical fibers is more accurate than the NLS equation. A study of high-order soliton matrix is…
The goal of this work is to revisit the eigenfunction-expansion-based perturbation theory for the defocusing nonlinear Schr\"odinger equation a nonzero background, and develop it to correctly predict the slow-time evolution of the dark…
Using the matrix Riemann-Hilbert factorisation approach for non-linear evolution equations (NLEEs) integrable in the sense of the inverse scattering method, we obtain, in the solitonless sector, the leading-order asymptotics as $t$ tends to…
We consider the inhomogeneous fifth-order nonlinear Schr\"{o}dinger (ifoNLS) equation with nonzero boundary condition in detailed. Firstly, the spectral analysis of the scattering problem is carried out. A Riemann surface and affine…
This paper is an expository account of the development of soliton mathematics, from its inception in famous numerical experiments of Fermi-Pasta-Ulam and Zabusky-Kruskal to the recent synthesis of Terng-Uhlenbeck (dg-ga/9707004) that…
In this paper, we report a more general class of nondegenerate soliton solutions, associated with two distinct wave numbers in different modes, for a certain class of physically important integrable two component nonlinear Schr\"{o}dinger…
We study a system of inhomogeneous nonlinear Schr\"odinger equations that emerge in optical media with a $\chi^{(2)}$ nonlinearity. This nonlinearity, whose local strength is subject to a cusp-shaped spatial modulation, $\chi^{(2)}\sim…
The nonlocal nonlinear evolution equations describe phenomena in which wave evolution is influenced by local and nonlocal spatial and temporal variables. These equations have opened up a new wave of physically important nonlinear evolution…
Inverse scattering problem for an operator, which is a sum of the operator of the third derivative and of an operator of multiplication by a real function, is solved. The main closed system of equations of inverse problem is obtained. This…
The light ray of a spatial soliton in an optical film whose refractive index is smoothly modulated (wavelength much larger than the typical soliton width) in both spatial directions is shown to possess chaotic regimes for which the…
In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model…
We derive a nonlinear Schroedinger equation with a radical term, in the form of the square root of (1-|V|^2), as an asymptotic model of the optical medium built as a periodic set of thin layers of two-level atoms, resonantly interacting…