Evolution of perturbed embedded solitons in the general Hamiltonian fifth-order Korteweg–de Vries (KdV) equation is studied. When an embedded soliton is perturbed, it sheds a one-directional continuous-wave radiation. It is shown that the radiation amplitude is not minimal in general. A dynamical equation for velocity of the perturbed embedded soliton is derived. This equation shows that a neut...

An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schrödinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the previously known soliton solutions of dark-bright pair. Here a dark soliton resides on a cnoidal wave instead of on a constant background. It also exhibits a new types...

Scattering of solitons and dark solitons by potential walls is studied in the nonlinear Schrödinger equation under various conditions. We investigate the conditions under which solitons are split into two solitons at the potential wall. We find that a soliton can be trapped in an interspace between two potential walls. A dark soliton can also be scattered at the potential wall. Similarly to a b...

We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of Multiple soliton solutions of secondorder Benjamin-Ono equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.

In this paper, we construct the Lax pair for a soliton transmission system in nonuniform optical fibers and give N-soliton solution using the Darboux transformation. The explicit one-soliton and two-soliton solutions are presented. Further, we discuss the interaction scenario between two neighboring solitons and the effect of the inhomogeneities of the fiber (z0) on the interaction between two ...

A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schrödinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton. Keywords—soliton, instability, variational method, spectral method

This work concerns itself on two new coupled mKdV systems, the first with time-dependent coefficients, and the second with constant coefficients. The soliton ansatz will be used for the first system to obtain 1-bright soliton solution. The simplified form of the bilinear method will be used to derive multiple-soliton solutions and multiple singular soliton solutions for the second coupled mKdV ...

The effect of walk-off in pattern selection in optical parametric oscillators is theoretically examined. We show that a dynamic mechanism also allows us to observe the formation of structures for positive signal detunings. In this regime the pattern that is generated is a periodic array of kinks that separate regions in which one of two stable steady states is alternately selected. This structu...

purpose: to report two cases of bilateral bacterial keratitis as a sight-threatening complication following photorefractive keratectomy (prk) patients and findings: the first case was a 45-year-old man referred due to bilateral ocular pain and purulent discharge two days after bilateral prk. based on his clinical picture, smear and cultures from both corneal ulcers were taken with a diagnosis o...

in a typical solitonic distribution, the soliton density is distributed over the entire moleculeand the present work shows how its density can be decomposed into solitonic and antisolitoniccomponents. it is found that there exists a unique electron as soliton over the anionicnanoconductor, while there are many other solitons and antisolitons. the solitonic states are furtherdecomposed to the ca...