4.7 Article

Optical solitons for the concatenation model: Power-law nonlinearity

Related references

Note: Only part of the references are listed.
Article Optics

Painlev? analysis and optical solitons for a concatenated model

Nikolay A. Kudryashov et al.

Summary: This paper applies Painleve analysis to a concatenated model combining the well-known nonlinear Schrodinger's equation, Lakshmanan-Porsezian-Daniel model, and Sasa-Satsuma equation. A bright 1-soliton solution is obtained using Jacobi's elliptic function as an intermediary.

OPTIK (2023)

Article Optics

Phase portraits and multiple optical solitons perturbation in optical fibers with the nonlinear Fokas-Lenells equation

Lu Tang

Summary: This paper focuses on the dynamical behavior and optical solitons in optical fibers with the nonlinear Fokas-Lenells equation. Dark solitons, periodic wave solutions, and bright solitons are analytically constructed using the bifurcation theory of planar dynamical systems. Other traveling wave solutions are also derived through the complete discriminant system technique and symbolic computation. Numerical results are provided to illustrate the physical properties of the obtained optical soliton solutions.

JOURNAL OF OPTICS-INDIA (2023)

Article Optics

Bifurcations, stationary optical solitons and exact solutions for complex Ginzburg-Landau equation with nonlinear chromatic dispersion in non-Kerr law media

Tianyong Han et al.

Summary: This paper transforms the complex Ginzburg-Landau equation (CGLE) into a second order nonlinear ordinary differential equation through an appropriate substitution, and obtains the bifurcation, stationary soliton solution and exact solution of CGLE by using dynamic system theory and polynomial complete discriminant system method. Abundant solutions are obtained, including periodic solutions, doubly-periodic solutions, hyperbolic function solutions, rational function solutions and exponential function solutions. Finally, the 3D and 2D graphics for the solutions are drawn. The research results provide a way to avoid the disaster of superconducting propagation in nonlinear media, as the appearance of stationary soliton means the stop of signal transmission.

JOURNAL OF OPTICS-INDIA (2023)

Article Optics

Novel soliton solutions of CNLSEs with Hirota bilinear method

Shaofu Wang

Summary: The coupled nonlinear Schrödinger equation in the (2 + 1)-dimensional inhomogeneous PT-symmetric nonlinear coupler is investigated. Soliton solutions are obtained using the Hirota bilinear method. The dynamics of localized structures, including periodic solitons, are analytically studied when dispersion and phase modulation coefficients are constant, exponential, and hyperbolic functions, respectively. The wave propagation collision is also discussed, and the interactions between two solitons propagating in different directions are analyzed. It has certain significance for the stable transmission of solitons in fiber couplers.

JOURNAL OF OPTICS-INDIA (2023)

Article Optics

Optical Solitons and traveling wave solutions to Kudryashov?s equation

S. A. Khuri et al.

Summary: This paper utilizes a generalized transformation to analyze Kudryashov's equation with four nonlinear terms, aiming to find traveling wave solutions and optical solitons. The proposed unified ansatz framework is employed to obtain analytical solutions, which are expressed as combinations of general solutions to simpler equations or systems of equations that are integrable or have known unique solutions. By using this technique, both families of new exact solutions and solitary solutions can be generated. Furthermore, the approach also reveals the presence of Jacobi, Weierstrass, and Riccati elliptic functions, which are classified as singular, bright, and dark optical solitons.

OPTIK (2023)

Article Optics

Exact solutions of an extended (3+1)-dimensional nonlinear Schr?dinger equation with cubic-quintic nonlinearity term

Gangwei Wang et al.

Summary: This paper investigates an extended (3+1)-dimensional nonlinear Schrodinger equation with a cubic-quintic nonlinearity term. By using the ansatz method, various exact solutions of this equation are obtained, including solitons, elliptic function solutions, and periodic function solutions. The relationships between these solutions and their coefficients are derived.

OPTIK (2023)

Article Optics

Bifurcations and optical solitons for the coupled nonlinear Schrodinger equation in optical fiber Bragg gratings

Lu Tang

Summary: This work focuses on studying bifurcations and dispersive optical solitons for the coupled nonlinear Schrodinger equation in optical fiber Bragg gratings. Using the bifurcation method of planar dynamical systems, the Hamiltonian of the system and the phase portraits of the orbits have been found. Dark and singular solitons are constructed for this system, along with other soliton solutions derived using the polynomial complete discriminant method and computer algebra. Some of these solutions are new and not found in existing references. The obtained soliton solutions substantially improve or complement the conditions in existing references. Two-dimensional and three-dimensional graphs are used to understand the complex physical phenomena and dynamical processes for this system.

JOURNAL OF OPTICS-INDIA (2023)

Article Physics, Mathematical

Propagation of electrostatic potential with dynamical behaviors and conservation laws of the (3+1)-dimensional nonlinear extended quantum Zakharov-Kuznetsov equation

Muhammad Junaid-U-Rehman et al.

Summary: The (G'/G)-expansion scheme is applied to study the wave results of the nonlinear extended quantum Zakharov-Kuznetsov equation in quantum electron-positron-ion magneto plasmas. The Lie approach is used to find the infinitesimal generators and group invariant solutions, reducing the partial differential equations into ordinary differential equations. A planar dynamical system approach is used to investigate the existence of closed-form solutions and obtain all possible phase portraits. Using the Runge-Kutta method, periodic and super-nonlinear electrostatic wave potentials are found under different initial value conditions. New traveling wave patterns of the considered models are constructed and illustrated graphically. Additionally, the conserved vectors of the given physical model are presented using the multiplier scheme.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS (2023)

Article Multidisciplinary Sciences

Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms

Muhammad Junaid-U-Rehman et al.

Summary: Nonlinear chains of atoms (NCA) are complex systems that can be analyzed using the Lie symmetry approach, which helps reduce complexity and obtain solutions by analyzing and solving differential equations with symmetries. The Lie scheme is used to find the optimal system of symmetries, and the multiplier method is applied to identify conservation laws.

SCIENTIFIC REPORTS (2023)

Article Optics

Optical solitons for the concatenation model with power-law nonlinearity: undetermined coefficients

Anjan Biswas et al.

Summary: In this paper, a complete range of 1-soliton solutions to the concatenation model with power-law self-phase modulation has been derived successfully using the method of undetermined coefficients. The resulting parameter constraints have been identified and listed, ensuring the existence of these solitons. It has been proven that specific types of dark solitons and singular solitons exist only when the power-law parameter equals unity.

UKRAINIAN JOURNAL OF PHYSICAL OPTICS (2023)

Article Optics

Painleve analysis and optical solitons for a concatenated model

Nikolay A. Kudryashov et al.

Summary: This paper applies Painleve analysis to a concatenated model consisting of the well-known nonlinear Schrodinger's equation, Lakshmanan-Porsezian-Daniel model, and Sasa-Satsuma equation. A bright 1-soliton solution is then obtained using the intermediary Jacobi's elliptic function.

OPTIK (2023)

Article Materials Science, Multidisciplinary

Optical solitons with perturbed complex Ginzburg-Landau equation in kerr and cubic-quintic-septic nonlinearity

Ming-Yue Wang

Summary: This paper presents exact solutions from perturbed complex Ginzburg-Landau equation with Kerr law and cubic-quintic-septic nonlinearity, using two approaches - the trial equation method and complete discriminant system for polynomial method. The obtained solutions can better analyze complex optical phenomena and demonstrate their essence effectively.

RESULTS IN PHYSICS (2022)

Article Mathematics, Interdisciplinary Applications

Multidimensional dissipative solitons and solitary vortices

B. A. Malomed

Summary: This article reviews the theoretical results of self-trapped states (solitons) in nonlinear dissipative media models, focusing on their stability and various formation mechanisms. The existence of these solitons relies on the balance between nonlinear self-focusing and linear spreading of the physical fields, as well as the balance between losses and gain in the medium. The article presents stable solitons in two- and three-dimensional models, including fundamental solitons, vortical solitons, and weakly localized states. It also discusses the effects of spatially modulated loss or gain and external potentials on the formation of dissipative solitons.

CHAOS SOLITONS & FRACTALS (2022)

Article Mathematics, Interdisciplinary Applications

Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation

Adil Jhangeer et al.

Summary: This paper investigates the nonlinear modified Gardner equation through Lie group analysis, converting partial differential equations into ordinary differential equations using similarity reduction method and constructing exact solutions using power series technique. The Galilean transformation is used to transform the model into a planar dynamical system, and various types of phase portraits are plotted with sensitivity analysis and the application of extrinsic periodic power to study the influence on the model's behavior.

CHAOS SOLITONS & FRACTALS (2021)

Article Mathematics, Applied

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

Nikolay A. Kudryashov

APPLIED MATHEMATICS AND COMPUTATION (2020)

Article Mathematics, Interdisciplinary Applications

Optical solitons of model with integrable equation for wave packet envelope

Nikolay A. Kudryashov

CHAOS SOLITONS & FRACTALS (2020)

Article Mathematics, Applied

Exact solutions of the equation for surface waves in a convecting fluid

Nikolay A. Kudryashov

APPLIED MATHEMATICS AND COMPUTATION (2019)

Article Mathematics, Interdisciplinary Applications

Two (2+1)-dimensional integrable nonlocal nonlinear Schrodinger equations: Breather, rational and semi-rational solutions

Yulei Cao et al.

CHAOS SOLITONS & FRACTALS (2018)

Article Optics

Dynamics of one-dimensional quantum droplets

G. E. Astrakharchik et al.

PHYSICAL REVIEW A (2018)

Article Optics

Two-dimensional dark solitons in diffusive nonlocal nonlinear media

Si-Liu Xu et al.

JOURNAL OF OPTICS-INDIA (2015)

Article Physics, Fluids & Plasmas

Extended nonlinear Schrodinger equation with higher-order odd and even terms and its rogue wave solutions

Adrian Ankiewicz et al.

PHYSICAL REVIEW E (2014)

Article Physics, Multidisciplinary

Higher-order integrable evolution equation and its soliton solutions

Adrian Ankiewicz et al.

PHYSICS LETTERS A (2014)

Article Engineering, Mechanical

Two-dimensional accessible solitons in PT-symmetric potentials

Wei-Ping Zhong et al.

NONLINEAR DYNAMICS (2012)

Article Mathematics, Interdisciplinary Applications

Solitary wave solutions for high dispersive cubic-quintic nonlinear Schrodinger equation

F. Azzouzi et al.

CHAOS SOLITONS & FRACTALS (2009)

Article Physics, Multidisciplinary

A new mapping method and its applications to nonlinear partial differential equations

Xin Zeng et al.

PHYSICS LETTERS A (2008)

Article Physics, Multidisciplinary

Gap solitons in Bragg gratings with dispersive reflectivity

J Atai et al.

PHYSICS LETTERS A (2005)

Review Physics, Multidisciplinary

Self-focusing and transverse instabilities of solitary waves

YS Kivshar et al.

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS (2000)