Wyniki wyszukiwania - BazTech

1

Localized optical vortex solitons in pair plasmas

Medina Luciano

Journal of Applied Analysis

|

2021

|

Vol. 27, nr 1

1--12

EN

The dynamics of short intense electromagnetic pulses propagating in a relativistic pair plasma is governed by a nonlinear Schrödinger equation with a new type of focusing-defocusing saturable nonlinearity. In this context, we provide an existence theory for ring-profiled optical vortex solitons. We prove the existence of both saddle point and minimum type solutions. Via a constrained minimization approach, we prove the existence of solutions where the photon number may be prescribed, and we get the nonexistence of small-photon-number solutions.We also use the constrained minimization to compute the soliton’s profile as a function of the photon number and other relevant parameters.

2

Solutions to a nonlinear Maxwell equation with two competing nonlinearities in R3

Bieganowski Bartosz

Bulletin of the Polish Academy of Sciences. Mathematics

|

2021

|

Vol. 69, no. 1

37--60

EN

We are interested in the nonlinear, time-harmonic Maxwell equation ∇(∇E)+V(x)E=h(x,E) in R3 with sign-changing nonlinear term h, i.e. we assume that h is of the form h(x,αw)=f(x,α)w−g(x,α)w for w∈R3, |w|=1 and α∈R. In particular, we can consider the nonlinearity consisting of two competing powers, h(x,E)=|E|p−2E−|E|q−2E with 2

3

Modulational instability of obliquely interacting capillary-gravity waves over infinite depth

Manna S., Dhar A. K.

Archives of Mechanics

|

2021

|

Vol. 73, nr 5-6

583--598

EN

Two coupled time-dependent two dimensional nonlinear Schrödinger equations have been derived using multiscale expansion for two nonlinearly interacting capillary-gravity waves over an infinite depth of water. These equations are then utilised to discuss the modulational (Benjamin-Feir) instability of two Stokes wavetrains due to unidirectional and bidirectional perturbations. It is found from the graphs and the three-dimensional contour plots that the rate of growth of instability for two wave packets interacting obliquely is higher than the instance of modulation of one wave packet. We have likewise examined the influence of capillarity on modulational instability.

4

Hasimoto surfaces for two classes of curve evolution in Minkowski 3-space

Gürbüz Nevin, Yoon Dae Won

Demonstratio Mathematica

|

2020

|

Vol. 53, nr 1

277--284

EN

In this work, we study Hasimoto surfaces for the second and third classes of curve evolution corresponding to a Frenet frame in Minkowski 3-space. Later, we derive two formulas for the differentials of the second and third Hasimoto-like transformations associated with the repulsive-type nonlinear Schrödinger equation.

5

Transformations and Soliton Solutions for a Variable-coefficient Nonlinear Schrödinger Equation in the Dispersion Decreasing Fiber with Symbolic Computation

Zeng Z.-F., Liu J.-G., Jiang Y., Nie B.

Fundamenta Informaticae

|

2016

|

Vol. 145, nr 2

207--219

EN

Describing the dispersion decreasing fiber, a variable-coefficient nonlinear Schrödinger equation is hereby under investigation. Three transformations have been obtained from such a equation to the known standard and cylindrical nonlinear Schrödinger equations with the relevant constraints on the variable coefficients presented, which turn out to be more general than those previously published in the literature. Meanwhile, several families of exact dark-soliton-like and bright-soliton-like solutions are constructed. Also, we obtain some similarity solutions, which can be illustrated in terms of the elliptic and the second Painlevé transcendent equations.

6

The transmission characteristics under the influence of the fifth-order nonlinearity management

He X., Xie K.

Optica Applicata

|

2012

|

Vol. 42, nr 1

103-110

EN

Starting with the nonlinear Schrödinger (NLS) equation, we have derived the evolution equations for the parameters of soliton pulse with propagation distance in optical fibers, taking into consideration the combined effect of second-order dispersion and the fifth-order nonlinearity by means of variation method. According to nonlinear evolution equations, the evolution of the pulse width with propagation distance is obtained under the influence of the different fifth-order nonlinearity. The results show that the pulse width fluctuates periodically under the influence of the different fifth-order nonlinearity. In the cycle, the negative fifth-order nonlinearity makes the pulse-width greater than the initial value while the positive fifth-order nonlinearity makes the pulse width less than the initial value. However, under the positive and negative fifth-order nonlinearity management, compared to the impact of positive or negative fifth-order nonlinearity only, the fluctuations of the solitons width are greatly reduced, even disappear. In other words, the width maintains almost steady. Therefore, it is possible that the pulse width is to be transmitted without any deformation.