Results 81 to 90 of about 1,989,001 (174)

Localized Dispersive States in Nonlinear Coupled Mode Equations for Light Propagation in Fiber Bragg Gratings. [PDF]

, 2009
Dispersion effects induce new instabilities and dynamics in the weakly nonlinear description of light propagation in fiber Bragg gratings. A new family of dispersive localized pulses that propagate with the group velocity is numerically found, and its ...
Martel Escobar, Carlos, Higuera, María, Carrasco, J.   +2 more
core   +1 more source

Nonlocal nonlinear Schrödinger equations and their soliton solutions

, 2018
We study standard and nonlocal nonlinear Schrödinger (NLS) equations obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur (AKNS) equations) by using standard and nonlocal reductions, respectively.
Pekcan, ASLI, Aslı Pekcan, Gürses, Metin, Metin Gürses, Pekcan, A.   +4 more
core   +1 more source

Existence and uniqueness solution analysis of time-fractional unstable nonlinear Schrödinger equation

Results in Physics
The time-fractional unstable nonlinear Schrödinger (NLS) equations capture the time evolution of disturbances within media, tailored for describing phenomena in unstable media to help model and understand the intricate dynamics of systems prone to ...
M. Ayesha Khatun, Mohammad Asif Arefin, M. Ali Akbar, M. Hafiz Uddin   +3 more
doaj   +1 more source

Rational Solutions to the Fourth Equation of the Nonlinear Schrödinger Hierarchy

AppliedMath
This study concerns the research of rational solutions to the hierarchy of the nonlinear Schrödinger equation. In particular, we are interested in the equation of order 4. Rational solutions to the fourth equation of the NLS hierarchy are constructed and
Pierre Gaillard
doaj   +1 more source

Global solutions of nonlinear Schrödinger equations

, 1999
This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrödinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed.
Bourgain, J, J. Bourgain
core   +1 more source

Analysis of complex nonlinear reaction-diffusion equations [PDF]

, 2008
A mathematical analysis has been carried out for some nonlinear reaction- diffusion equations on open bounded convex domains Ω C R(^d)(d < 3) with Robin boundary conditions- Existence, uniqueness and continuous dependence on initial data of weak and ...
Al-Ofl, Abdalaziz Saleem
core  

Propagation of wave insights to the Chiral Schrödinger equation along with bifurcation analysis and diverse optical soliton solutions

Alexandria Engineering Journal
In this study, the modified Sardar sub-equation (MSSE) method is capitalized to secure soliton solutions to the (1+1)-dimensional chiral nonlinear Schrödinger (NLS) equation.
Badr Saad T. Alkahtani
doaj   +1 more source

On the covering dimension of the set of solutions of some nonlinear equations [PDF]

, 1986
We prove an abstract theorem whose sole hypothesis is that the degree of a certain map is nonzero and whose parametric equations are studied using cohomological mconclusions imply sharp, multidimensional continuation results.
Pejsachowicz, Jacobo, Fitzpatrick, P., Massabò, I., Fitzpatrick P., Massabò I.   +4 more
core  

Numerical methods for a class of generalized nonlinear schrödinger equations

, 2015
We present and analyze different splitting algorithms for numerical solution of the both classical and generalized nonlinear Schrödinger equations describing propagation of wave packets with special emphasis on applications to nonlinear fiber-optics. The
Amiranashvili, Shalva, Čiegis, Raimondas, Radziunas, Mindaugas   +2 more
core   +1 more source

A $\overline{\partial }$-Dressing Method for the Kundu-Nonlinear Schrödinger Equation

Mathematics
In this paper, we employed the ∂¯-dressing method to investigate the Kundu-nonlinear Schrödinger equation based on the local 2 × 2 matrix ∂¯ problem. The Lax spectrum problem is used to derive a singular spectral problem of time and space associated with
Jiawei Hu, Ning Zhang
doaj   +1 more source