Abundant traveling wave solutions to an intrinsic fractional discrete nonlinear electrical transmission line

Chen, Shuangqing; Li, Yuchun; Jiang, Minghu; Guan, Bing; Bu, Fanxi

doi:10.1016/j.rinp.2021.104587

Cited by 9 publications

(3 citation statements)

References 52 publications

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“…Fractional-order circuit theory is also developing rapidly, and has been applied to lithium-ion batteries [21], electrical transmission lines [22], etc. The design and implementation of fractional-order components have been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Fractional circuit network theory with n-V-structure

Luo

Tan

2023

Phys. Scr.

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This paper studies a class of circuit network model with fractional n-V-structure, the model contains several independent resistance elements, so it is the topology of multiple network models. First, this paper calculates the equivalent resistance of n-V circuit network by constructing equivalent model, and gives two closed equivalent resistance analytic expressions. Additionally, the concept of negative resistance is put forward. A series of special results of equivalent resistance are discussed. Finally, the complex impedance characteristics of fractional n-V structure circuit networks are studied in detail by using variable substitution technique. The amplitude frequency characteristics and phase frequency characteristics of fractional n-V structure circuit network are revealed through Matlab drawing research.

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Section: Introductionmentioning

confidence: 99%

Fractional circuit network theory with n-V-structure

Luo

Tan

2023

Phys. Scr.

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“…The CDSPM is proposed by Liu [25][26][27] and has been successfully applied to a series of integer-order [28,29] and fractional-order equations [30][31][32][33][34]. Then, Kai et al found that this method could also be used to conduct qualitative analysis [35], and combining with the bifurcation method, we can even establish the existence of the soliton and periodic solution [36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions and Dynamic Properties of the Perturbed Nonlinear Schrödinger Equation with Conformable Fractional Derivatives Arising in Nanooptical Fibers

Shu-xin

Chen

2022

Advances in Mathematical Physics

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The main idea of this paper is to investigate the exact solutions and dynamic properties of a space-time fractional perturbed nonlinear Schrödinger equation involving Kerr law nonlinearity with conformable fractional derivatives. Firstly, by the complex fractional traveling wave transformation, the traveling wave system of the original equation is obtained, then a conserved quantity, namely, the Hamiltonian, is constructed, and the qualitative analysis of this system is conducted via this quantity by classifying the equilibrium points. Moreover, the existences of the soliton and periodic solution are established via the bifurcation method. Furthermore, all exact traveling wave solutions are constructed to illustrate our results explicitly by the complete discrimination system for the polynomial method.

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“…All conditions of parameters are discussed, thus this paper contains all results of traveling wave solutions in the existing literatures, and some new solutions are obtained. The CDSPM is proposed by Liu [10][11][12], and has been successfully applied to a series of integerorder [13][14] and fractional order equations [15][16][17][18][19]. Then Kai found that this method could also be used to conduct qualitative analysis [20], and combining with the bifurcation method, we can even establish the existence of the soliton and periodic solution [21].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions and Dynamic Properties of Perturbed Nonlinear Schrodinger Equation Arised From Nano Optical Fibers

Xin¹,

Chen²

2021

Preprint

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The main idea of this paper is to investigate the exact solutions and dynamic properties in optical nanofibers, which is modeled by space-time fractional perturbed nonlinear schr\"odinger equation involving Kerr law nonlinearity with conformal fractional derivative. Firstly, by the complex fractional traveling wave transformation, the traveling wave system of the original equation is obtained, then a conserved quantity, namely the Hamiltonian is constructed, and the qualitative analysis of this system is conducted via this quantity by classifying the equilibrium points. Moreover, the prior estimate of the existence of the soliton and periodic solution is established via the bifurcation method. Furthermore, all exact traveling wave solutions are constructed to illustrate our results explicitly by the complete discrimination system for polynomial method.

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Abundant traveling wave solutions to an intrinsic fractional discrete nonlinear electrical transmission line

Cited by 9 publications

References 52 publications

Fractional circuit network theory with n-V-structure

Fractional circuit network theory with n-V-structure

Exact Solutions and Dynamic Properties of the Perturbed Nonlinear Schrödinger Equation with Conformable Fractional Derivatives Arising in Nanooptical Fibers

Exact Solutions and Dynamic Properties of Perturbed Nonlinear Schrodinger Equation Arised From Nano Optical Fibers

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Abundant traveling wave solutions to an intrinsic fractional discrete nonlinear electrical transmission line

Cited by 9 publications

References 52 publications

Fractional circuit network theory with n-V-structure

Fractional circuit network theory with n-V-structure

Exact Solutions and Dynamic Properties of the Perturbed Nonlinear Schrödinger Equation with Conformable Fractional Derivatives Arising in Nanooptical Fibers

Exact Solutions and Dynamic Properties of Perturbed Nonlinear Schrodinger Equation Arised From Nano Optical Fibers

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Exact Solutions and Dynamic Properties of Perturbed Nonlinear Schrodinger Equation Arised From Nano Optical Fibers