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Qi, Jianming; Cui, Qinghua; Zhang, Le; Sun, Yiqun

Solution structures of an electrical transmission line model with bifurcation and chaos in Hamiltonian dynamics. (English) Zbl 1541.35481

Int. J. Bifurcation Chaos Appl. Sci. Eng. 33, No. 9, Article ID 2350108, 34 p. (2023).

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
78A40 Waves and radiation in optics and electromagnetic theory
35C08 Soliton solutions
35C05 Solutions to PDEs in closed form
35B32 Bifurcations in context of PDEs
35A24 Methods of ordinary differential equations applied to PDEs
34H10 Chaos control for problems involving ordinary differential equations
33E05 Elliptic functions and integrals
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
26A33 Fractional derivatives and integrals
35R11 Fractional partial differential equations

Keywords:

fraction order; phase portrait; bifurcation; chaotic behavior; nonlinear electrical transmission; Weierstrass elliptic function
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Full Text: DOI

References:

[1] Abdou, M. A. & Elgarayhi, A. [2015] “ On the nonlinear difference-differential equations arising in physics,” J. Assoc. Arab Univ. Basic Appl. Sci.18, 89-93.
[2] Abdou, M. A. & Soliman, A. A. [2018] “ New exact traveling wave solutions for space-time fractional nonlinear equations describing nonlinear transmission lines,” Results Phys.9, 1497-1501.
[3] Abdoulkary, S.et al. [2014] “ Exact solutions of the nonlinear differential-difference equations associated with the nonlinear electrical transmission line through a variable-coefficient discrete \(( \frac{ G^\prime}{ G} )\)-expansion method,” Chinese Phys. B, 120506.
[4] Abdoulkary, S.et al. [2015] “ Solitary wave solutions and modulational instability analysis of the nonlinear Schrödinger equation with higher-order nonlinear terms in the left-handed nonlinear transmission lines,” Commun. Nonlin. Sci.22, 1288-1296. · Zbl 1334.35012
[5] Alabedalhadi, M. [2022] “ Exact traveling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations,” Alex. Eng. J.61, 1033-1044.
[6] Ambassa, G. B.et al. [2016] “ Wave solitons in a coupled left-handed nonlinear transmission line: Effect of the coupling parameter,” Chaos Solit. Fract.91, 400-405. · Zbl 1372.35066
[7] Ashraf, F.et al. [2022] “ Multi-wave, M-shaped rational and interaction solutions for fractional nonlinear electrical transmission line equation,” J. Geom. Phys.177, 104503. · Zbl 1489.35267
[8] Aslan, I. [2016] “ Exact solutions for a local fractional DDE associated with a nonlinear transmission line,” Commun. Theor. Phys.9, 57-62. · Zbl 1351.34095
[9] Aziz, F., Asif, A. & BinteMunir, F. [2020] “ Analytical modeling of electrical solitons in a nonlinear transmission line using Schamel-Korteweg deVries equation,” Chaos Solit. Fract.134, 109737. · Zbl 1483.35181
[10] Bodo, B., Mvogo, A. & Morfu, S. [2017] “ Fractional dynamical behavior of electrical activity in a model of pancreatic \(\beta \)-cells,” Chaos Solit. Fract.102, 426-432.
[11] Chaudhuri, S.et al. [2017] “ Broadband parametric amplifiers based on nonlinear kinetic inductance artificial transmission lines,” Appl. Phys. Lett.110, 152-601.
[12] Chen, Y. & Yan, Z. Y. [2003] “ The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations,” Chaos Solit. Fract.29, 948-964. · Zbl 1142.35603
[13] Fan, E. G. [2003] “ Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics,” Chaos Solit. Fract.16, 819-839. · Zbl 1030.35136
[14] Fendzi-Donfack, E., Nguenang, J. P. & Nana, L. [2018] “ Fractional analysis for nonlinear electrical transmission line and nonlinear Schrödinger equations with incomplete sub-equation,” Eur. Phys. J. Plus133, 32. · Zbl 1495.35189
[15] Fendzi-Donfack, E., Nguenang, J. P. & Nana, L. [2020] “ On the traveling waves in nonlinear electrical transmission lines with intrinsic fractional-order using discrete tanh method,” Chaos Solit. Fract.131, 109486. · Zbl 1495.35189
[16] Fendzi-Donfack, E., Nguenang, J. P. & Nana, L. [2021] “ On the soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission line,” Nonlin. Dyn.104, 691-704.
[17] Fendzi-Donfack, E.et al. [2023] “ Dynamical behaviours and fractional alphabetical-exotic solitons in a coupled nonlinear electrical transmission lattice including wave obliqueness,” Opt. Quant. Electron.55, 35.
[18] Ganji, D. D., Nourollahi, M. & Mohseni, E. [2007] “ Application of He’s methods to nonlinear chemistry problems,” Comput. Math. Appl.54, 1122-1132. · Zbl 1267.65100
[19] Halidou, H.et al. [2022] “ Rational w-shape solitons on a nonlinear electrical transmission line with Josephson junction,” Phys. Lett. A430, 127951. · Zbl 1486.81096
[20] Indirayanti, P.et al. [2012] “ Picosecond pulse generation with nonlinear transmission lines in \(90\) nm CMOS for mm-wave imaging applications,” 2012 19th IEEE Int. Conf. Electronics, Circuits, and Systems (ICECS 2012), pp. 885-888.
[21] Jonscher, A. K. [1993] Dielectric Relaxation in Solids (Chelsea Dielectric Press, London).
[22] Kayum, M. A., Ara, S., Barman, H. K. & Akbar, M. A. [2020] “ Soliton solutions to voltage analysis in nonlinear electrical transmission lines and electric signals in telegraph lines,” Results Phys.18, 103269.
[23] Kenmogne, F. & Yemélé, D. [2012] “ Exotic modulated signals in a nonlinear electrical transmission line: Modulated peak solitary wave and gray compacton,” Chaos Solit. Fract.45, 21-34.
[24] Kenmogne, F.et al. [2015] “ Nonlinear supratransmission in a discrete nonlinear electrical transmission line: Modulated gap peak solitons,” Chaos Solit. Fract.75, 263-271. · Zbl 1352.94095
[25] Lawden, D. F. [1989] Elliptic Functions and Applications, , Vol. 80 (Springer, NY), pp. 1-349. · Zbl 0689.33001
[26] Mbouna Ngueuteu, G. S. & Woafo, P. [2012] “ Dynamics and synchronization analysis of coupled fractional-order nonlinear electromechanical systems,” Mech. Res. Commun.46, 20-25.
[27] Narahara, K. [2018] “ Modulation of pulse train using leapfrogging pulses developed in unbalanced coupled nonlinear transmission lines,” Math. Probl. Eng.7, 2869731. · Zbl 1426.94076
[28] Ndzana, F. I., Djelah, G. & Mohamadou, A. [2022] “ Solitonic rogue waves dynamics in a nonlinear electrical transmission line with the next nearest neighbor couplings,” Chinese J. Phys.77, 1927-1945. · Zbl 1540.35377
[29] Nkongho, A. A., Dikandé, A. M. & Mbobda, C. R. F. [2022] “ Solitary-wave dynamics in an \(R^2LC\) nonlinear transmission line with voltage bias,” Results Phys.35, 105303.
[30] Nuruzzaman, M., Kumar, D. & Paul, G. C. [2021] “ Fractional low-pass electrical transmission line model: Dynamic behaviors of exact solutions with the impact of fractionality and free parameters,” Results Phys.27, 104457.
[31] Schafer, I. & Kruger, K. [2008] “ Modeling of lossy coils using fractional derivatives,” J. Phys. D41, 1-8.
[32] Seadawy, A. R., Iqbal, M. & Baleanu, D. [2020] “ Construction of traveling and solitary wave solutions for wave propagation in nonlinear low-pass electrical transmission lines,” J. King. Saud. Univ. Sci.32, 2752-2761.
[33] Shi, L. F. & Zhou, X. C. [2022] “ Exact solutions of a coupled space-time fractional nonlinear Schrödinger type equation in quantum mechanics,” Results Phys.42, 105967.
[34] Tacha, O. I.et al. [2016] “ Analysis, adaptive control and circuit simulation of a novel nonlinear finance system,” Appl. Math. Comput.276, 200-217. · Zbl 1410.91496
[35] Tala-Tebue, E.et al. [2014] “ Envelope periodic solutions for a discrete network with the Jacobi elliptic functions and the alternative \(( \frac{ G^\prime}{ G} )\)-expansion method including the generalized Riccati equation,” Eur. Phys. J. Plus129.
[36] Tchier, F.et al. [2017] “ Soliton solutions and conservation laws for lossy nonlinear transmission line equation,” Superlattice. Microst.107, 320-336.
[37] Togueu Motcheyo, A. B.et al. [2017] “ Chameleon’s behavior of modulable nonlinear electrical transmission line,” Commun. Nonlin. Sci.53, 22-30. · Zbl 1510.78010
[38] Wang, K. J. & Wang, G. D. [2021] “ Periodic solution of the \((2+1)\)-dimensional nonlinear electrical transmission line equation via variational method,” Results Phys.20, 103666.
[39] Westerlund, S. & Ekstam, L. [1994] “ Capacitor theory,” IEEE. Trans. Dielectr. Electr. Insul.1, 826-839.
[40] Xie, M.et al. [2014] “ Application of photochemical indicators to evaluate ozone nonlinear chemistry and pollution control countermeasure in China,” Atmos. Environ.99, 466-473.
[41] Yang, X. F.et al. [2015] “ A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application,” Adv. Diff. Eqs.1, 117-133. · Zbl 1422.35153
[42] Zhang, S.et al. [2009] “ The \(( \frac{ G^\prime}{ G} )\)-expansion method for nonlinear differential-difference equations,” Phys. Lett. A373, 905-910. · Zbl 1228.34096
[43] Zheng, B.et al. [2019] “ Exact traveling and non-traveling wave solutions of the time fractional reaction-diffusion equation,” Physica A532, 121780. · Zbl 1532.35507
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