4.7 Article

Highly Dispersive Optical Solitons with Complex Ginzburg-Landau Equation Having Six Nonlinear Forms

Related references

Note: Only part of the references are listed.
Article Mathematics, Applied

Solitary waves described by a high-order system in optical fiber Bragg gratings with arbitrary refractive index

Kristina Kan et al.

Summary: A system of fourth-order nonlinear differential equations for wave propagation in optical fiber Bragg gratings is considered, taking into account arbitrary refractive index and non-local nonlinearity. The system is transformed into ordinary differential equations using traveling wave variables, and compatibility conditions for the system are defined and analyzed. Exact solutions in the form of solitary waves are found.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2022)

Article Mathematics, Applied

The generalized Duffing oscillator

Nikolay A. Kudryashov

Summary: A study on the integrability of a generalized Duffing oscillator shows that it only passes the Painlevetest in the case of the classic Duffing oscillator described by a second-order differential equation. By expanding the general solution, exact solutions for the generalized Duffing oscillator with two arbitrary constants are found.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2021)

Article Optics

Discrete localized excitations for discrete conformable fractional cubic-quintic Ginzburg-Landau model possessing the non-local quintic term

Da-Sheng Mou et al.

Summary: By considering the conformable fractional derivative to modify the Jacobian elliptic function method, rich exact solutions of discrete conformable fractional complex cubic-quintic Ginzburg-Landau model with non-local quintic term are derived, showing different properties from their continuous analogs. The study also investigates the effects of filter and linear dissipation parameters on explosion excitation and wave amplitude modulation.

OPTIK (2021)

Article Engineering, Multidisciplinary

New Exact Solutions of the Fractional Complex Ginzburg-Landau Equation

Chun Huang et al.

Summary: This paper explores the exact solutions of the fractional complex Ginzburg-Landau equation and numerical simulations of optical pulse propagation in optic fibers. New exact solutions are obtained using the complete discrimination system method, including solitary wave solutions, rational function solutions, triangle function solutions, and Jacobian elliptic function solutions.Comparisons are made between previous results and the findings of this study.

MATHEMATICAL PROBLEMS IN ENGINEERING (2021)

Article Materials Science, Multidisciplinary

Conservation laws for pure-cubic optical solitons with complex Ginzburg-Landau equation having several refractive index structures

Anjan Biswas et al.

Summary: This paper discusses the conserved densities and quantities for the perturbed complex Ginzburg-Landau model using Lie symmetry analysis, and finds that for certain nonlinear forms, the Hamiltonian ceases to exist due to divergent integrals.

RESULTS IN PHYSICS (2021)

Article Optics

Solitary waves of the non-local Schrodinger equation with arbitrary refractive index

Nikolay A. Kudryashov

Summary: A new generalization of the nonlinear Schrödinger equation is presented, taking into account arbitrary reflective index in optical fiber and non-local nonlinearity. Exact solutions in the form of solitary waves, which can be considered as optical solitons, are derived. Special cases of the equation and its solutions are also considered.

OPTIK (2021)

Article Engineering, Electrical & Electronic

Pure-Cubic Optical Soliton Perturbation with Complex Ginzburg-Landau Equation Having a Dozen Nonlinear Refractive Index Structures

Elsayed M. E. Zayed et al.

Summary: This paper successfully recovers soliton solutions to perturbed pure-cubic complex Ginzburg-Landau equation using two integration schemes, namely the new mapping method and the addendum to Kudryashov's approach. Bright, dark, and singular soliton solutions are obtained for each nonlinear form, with periodic solutions emerging as a byproduct of the schemes.

JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS (2021)

Article Mathematics, Applied

Solitary wave solutions of hierarchy with non-local nonlinearity

Nikolay A. Kudryashov

APPLIED MATHEMATICS LETTERS (2020)

Article Mathematics, Applied

Highly dispersive solitary wave solutions of perturbed nonlinear Schrodinger equations

Nikolay A. Kudryashov

APPLIED MATHEMATICS AND COMPUTATION (2020)

Article Physics, Multidisciplinary

Periodic and solitary waves in optical fiber Bragg gratings with dispersive reflectivity

Nikolay A. Kudryashov

CHINESE JOURNAL OF PHYSICS (2020)

Article Mathematics, Applied

First integrals and general solution of the complex Ginzburg-Landau equation

Nikolay A. Kudryashov

APPLIED MATHEMATICS AND COMPUTATION (2020)

Article Mathematics, Applied

Highly Dispersive Optical Solitons of an Equation with Arbitrary Refractive Index

Nikolay A. Kudryashov

REGULAR & CHAOTIC DYNAMICS (2020)

Article Physics, Multidisciplinary

Generation of stable multi-vortex clusters in a dissipative medium with anti-cubic nonlinearity

Yunli Qiu et al.

PHYSICS LETTERS A (2019)

Article Mathematics

On a nonlocal problem involving a nonstandard nonhomogeneous differential operator

Mustafa Avci et al.

JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS (2019)

Article Engineering, Multidisciplinary

Solving generalized quintic complex Ginzburg-Landau equation by homotopy analysis method

Soheila Naghshband et al.

AIN SHAMS ENGINEERING JOURNAL (2018)

Article Engineering, Electrical & Electronic

TEMPORAL SOLITONS OF MODIFIED COMPLEX GINZBURG LANDAU EQUATION

S. Shwetanshumala

PROGRESS IN ELECTROMAGNETICS RESEARCH LETTERS (2008)

Article Mathematics, Applied

Explicit and implicit solutions for the one-dimensional cubic and quintic complex Ginzburg-Landau equations

Abdul-Majid Wazwaz

APPLIED MATHEMATICS LETTERS (2006)

Article Physics, Multidisciplinary

Solitary pulses and periodic waves in the parametrically driven complex Ginzburg-Landau equation

H Sakaguchi et al.

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN (2003)