Painlevé analysis, Lie group analysis and soliton-cnoidal, resonant, hyperbolic function and rational solutions for the modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics

Liu, Fei-Yan; Gao, Yi–Tian; Yu, Xin; Ding, Chaoliang; Deng, Gao-Fu; Jia, Ting-Ting

doi:10.1016/j.chaos.2020.110559

Cited by 73 publications

(6 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, a DDT for system(1) can be acquired as 4 Modulation instability has been the process of classifying the qualitative behavior of modulated waves, which is related to the growth of periodic disturbances on an unstable continuous wave background [23][24][25]. 5 Breather has been generated through the instability of the small amplitude disturbance [26,27].…”

Section: Ddt For System(1)mentioning

confidence: 99%

Darboux-dressing transformation, semi-rational solutions, breathers and modulation instability for the cubic-quintic nonlinear Schrödinger system with variable coefficients in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide

Yang

Tian

et al. 2021

Phys. Scr.

View full text Add to dashboard Cite

Twin-core optical fibers are applied in the fiber optic sensing technique and optical communication. Non-Kerr media are seen in plasma physics, nonlinear quantum mechanics and nonlinear optics. Propagation of an optical beam and superradiance for an atom in the waveguide are reported. This paper investigates the cubic-quintic nonlinear Schrödinger system with variable coefficients for the ultrashort optical pulse propagation in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide. For the two components of the electromagnetic fields, Darboux-dressing transformation, semi-rational solutions and breather solutions are obtained. We acquire the Akhmediev breathers (ABs) and Kuznetsov-Ma (KM) solitons. Interaction between the rogue waves and KM/bright-dark solitons is presented. When b(z) is a linear/quadratic/cosine function, the ABs, rogue waves, KM and bright-dark solitons appear parabolic, cubic and wavy, respectively, where b(z) presents the delayed nonlinear response effects. We conduct the modulation instability for the plane wave solutions for a non-Kerr medium, twin-core nonlinear optical fiber or waveguide via the linear stability analysis: If χ < 0, the solutions are modulationally stable; otherwise, modulationally unstable, where χ is the growth rate of the instability.

show abstract

Section: Ddt For System(1)mentioning

confidence: 99%

Darboux-dressing transformation, semi-rational solutions, breathers and modulation instability for the cubic-quintic nonlinear Schrödinger system with variable coefficients in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide

Yang

Tian

et al. 2021

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Lie group method is an effective way to find invariant solutions and to explore certain properties by reducing the dimensionality of the equations [14]. It has been described in sufficient detail in many literatures [15][16][17][18]. To begin with, we suppose that the one-parameter ðεÞ Lie group in Equation ( 1) is…”

Section: Lie Classical Symmetry Analysis Of Vcblpmentioning

confidence: 99%

Lie Symmetry Analysis, Exact Solutions, and Conservation Laws of Variable-Coefficients Boiti-Leon-Pempinelli Equation

Zhang

Xin

2021

Advances in Mathematical Physics

View full text Add to dashboard Cite

In this article, we study the generalized ( 2 + 1 )-dimensional variable-coefficients Boiti-Leon-Pempinelli (vcBLP) equation. Using Lie’s invariance infinitesimal criterion, equivalence transformations and differential invariants are derived. Applying differential invariants to construct an explicit transformation that makes vcBLP transform to the constant coefficient form, then transform to the well-known Burgers equation. The infinitesimal generators of vcBLP are obtained using the Lie group method; then, the optimal system of one-dimensional subalgebras is determined. According to the optimal system, the ( 1 + 1 )-dimensional reduced partial differential equations (PDEs) are obtained by similarity reductions. Through G ′ / G -expansion method leads to exact solutions of vcBLP and plots the corresponding 3-dimensional figures. Subsequently, the conservation laws of vcBLP are determined using the multiplier method.

show abstract

“…It is extensively taken that the integrable model must have Lax pair, Hamiltonian and bi-Hamiltonian structure, N-soliton solutions, infinitely many symmetries, bilinear Bäcklund transformation, etc. Painlevé analysis is a powerful procedure that can be utilized to examine the integrability [73][74][75].…”

Section: Introductionmentioning

confidence: 99%

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

Elmandouh

Elbrolosy

2022

Journal of Mathematics

View full text Add to dashboard Cite

The Ivancevic option pricing model comes as an alternative to the Black-Scholes model and depicts a controlled Brownian motion associated with the nonlinear Schrodinger equation. The applicability and practicality of this model have been studied by many researchers, but the analytical approach has been virtually absent from the literature. This study intends to examine some dynamic features of this model. By using the well-known ARS algorithm, it is demonstrated that this model is not integrable in the Painlevé sense. He’s variational method is utilized to create new abundant solutions, which contain the bright soliton, bright-like soliton, kinky-bright soliton, and periodic solution. The bifurcation theory is applied to investigate the phase portrait and to study some dynamical behavior of this model. Furthermore, we introduce a classification of the wave solutions into periodic, super periodic, kink, and solitary solutions according to the type of the phase plane orbits. Some 3D-graphical representations of some of the obtained solutions are displayed. The influence of the model’s parameters on the obtained wave solutions is discussed and clarified graphically.

show abstract

Painlevé analysis, Lie group analysis and soliton-cnoidal, resonant, hyperbolic function and rational solutions for the modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics

Cited by 73 publications

References 52 publications

Darboux-dressing transformation, semi-rational solutions, breathers and modulation instability for the cubic-quintic nonlinear Schrödinger system with variable coefficients in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide

Darboux-dressing transformation, semi-rational solutions, breathers and modulation instability for the cubic-quintic nonlinear Schrödinger system with variable coefficients in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide

Lie Symmetry Analysis, Exact Solutions, and Conservation Laws of Variable-Coefficients Boiti-Leon-Pempinelli Equation

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

Contact Info

Product

Resources

About