Phase portrait, sensitivity and chaotic analysis, variational principle, Hamiltonian and abundant wave solutions of the pulse narrowing transmission line model
-
Feng Zhao [1] ; Lu Zhang [1]
-
[1] Jiaozuo University
Jiaozuo University
China
-
- Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 44, Nº 4, 2025, págs. 660-675
- Idioma: inglés
- DOI: 10.1108/COMPEL-01-2025-0040
- Enlaces
-
Resumen
Purpose The purpose of this paper is to give a detailed and in-depth research on the pulse narrowing transmission lines model qualitatively and quantitatively.
Design/methodology/approach Applying the traveling wave transformation and semi-inverse method, the variational principle is established, and the Hamiltonian is extracted. The planar dynamical system is derived, then the phase portraits are plotted, and the bifurcation analysis is presented to discuss the existence conditions of the wave solutions with the different shapes. Furthermore, the chaotic phenomenon is probed via introducing the perturbed term, and the sensitivity analysis is given. Finally, the Hamiltonian-based method that is based on the energy conservation, as well as the variational method that originates from the variational principle and Ritz method, are adopted to develop the different wave solutions.
Findings According to the theory of planar systems, the discussion on the existence conditions of the wave solutions with different wave shapes reveals that the considered model has bell-shaped solitary wave and periodic wave solutions. Meanwhile, it is found that the small changes in initial conditions can have a significant impact on the behavior of the solution. Furthermore, diverse wave solutions such as bell-shaped solitary waves, anti-bell-shaped solitary waves and periodic wave solutions are obtained by the variational method and Hamiltonian-based method, which are consistent with the discussion on the conditions for the existence of wave solutions with the different wave shapes.
Originality/value To the best of the authors’ knowledge, the variational principle and Hamiltonian are first reported. The variational method and Hamiltonian-based method are first used to probe the diverse wave solutions. The qualitative analysis is presented to explore the dynamics of the model. The findings of this research are hoped to open some new perspectives toward the dynamics of the model under consideration.
-
Referencias bibliográficas
- Aderyani, S.R., Saadati, R., Vahidi, J. and Allahviranloo, T. (2022), “The exact solutions of the conformable Time-Fractional modified nonlinear...
- Afshari, E. and Hajimiri, A. (2005), “Nonlinear transmission lines for pulse shaping in silicon”, IEEE Journal of Solid-State Circuits, Vol....
- Afshari, E., Bhat, H.S., Hajimiri, A. and Marsden, J.E. (2006), “Extremely wideband signal shaping using one-and two-dimensional non-uniform...
- Akram, G., Sadaf, M. and Khan, M.A.U. (2022), “Soliton dynamics of the generalized shallow water like equation in nonlinear phenomenon”, Frontiers...
- Ali, M.R., Khattab, M.A. and Mabrouk, S.M. (2023), “Travelling wave solution for the Landau-Ginburg-Higgs model via the inverse scattering...
- Alizadeh, F., Hosseini, K., Sirisubtawee, S. and Hincal, E. (2024), “Classical and non-classical lie symmetries, bifurcation analysis, and...
- Bai, Y.S., Zheng, L.N., Ma, W.X. and Yun, Y.S. (2024), “Hirota bilinear approach to multi-component nonlocal nonlinear Schrödinger equations”,...
- Darwish, A., Ahmed, H.M., Arnous, A.H. and Shehab, M.F. (2021), “Optical solitons of Biswas-Arshed equation in birefringent fibers using improved...
- Gkogkou, A., Prinari, B., Feng, B.F. and Trubatch, A.D. (2022), “Inverse scattering transform for the complex coupled short-pulse equation”,...
- He, J.H. (2002), “Preliminary report on the energy balance for nonlinear oscillations. Mechanics research communications”, Mechanics Research...
- Hosseini, K., Hinçal, E. and Ilie, M. (2023a), “Bifurcation analysis, chaotic behaviors, sensitivity analysis, and soliton solutions of a...
- Hosseini, K., Hincal, E., Mirzazadeh, M., Salahshour, S., Obi, O.A. and Rabiei, F. (2023b), “A nonlinear Schrödinger equation including the...
- Kumar, D., Seadawy, A.R. and Chowdhury, R. (2018), “On new complex soliton structures of the nonlinear partial differential equation describing...
- Kumar, S., Kumar, A. and Kharbanda, H. (2021), “Abundant exact closed-form solutions and solitonic structures for the double-chain deoxyribonucleic...
- Li, W.L., Chen, S.H. and Wang, K.J. (2025), “A variational principle of the nonlinear Schrödinger equation with fractal derivatives”, Fractal,...
- Liang, Y.H. and Wang, K.J. (2025), “Diverse wave solutions to the new extended (2+1)-dimensional nonlinear evolution equation: phase portrait,...
- Liang, Y.H., Wang, K.J. and Hou, X.Z. (2025), “Multiple kink soliton, breather wave, interaction wave and the travelling wave solutions to...
- Liu, J.H., Yang, Y.N., Wang, K.J. and Zhu, H.W. (2025), “On the variational principles of the Burgers-Korteweg-de Vries equation in fluid...
- Ma, H.C. (2005), “A simple method to generate lie point symmetry groups of the (3+ 1)-dimensional Jimbo–Miwa equation”, Chinese Physics...
- Ma, W.X. (2022), “A novel kind of reduced integrable matrix mKdV equations and their binary Darboux transformations”, Modern Physics Letters...
- Ma, Y.X., Tian, B., Qu, Q.X., Yang, D.Y. and Chen, Y.Q. (2021), “Painlevé analysis, bäcklund transformations and traveling-wave solutions...
- Mohanty, S.K., Kravchenko, O.V., Deka, M.K., Dev, A.N. and Churikov, D.V. (2023), “The exact solutions of the 2+ 1–dimensional Kadomtsev–Petviashvili...
- Mostafa, S.I. (2009), “Analytical study for the ability of nonlinear transmission lines to generate solitons”, Chaos, Solitons and Fractals,...
- Onder, I., Secer, A., Ozisik, M. and Bayram, M. (2022), “On the optical soliton solutions of Kundu-Mukherjee-Naskar equation via two different...
- Raza, N. and Javid, A. (2019), “Optical dark and dark-singular soliton solutions of (1+2)-dimensional chiral nonlinear Schrodinger’s equation”,...
- Ullah, N., Asjad, M.I., Hussanan, A., Akgül, A., Alharbi, W.R., Algarni, H. and Yahia, I.S. (2023), “Novel waves structures for two nonlinear...
- Wang, K.L. (2024), “New computational approaches to the fractional coupled nonlinear Helmholtz equation”, Engineering Computations, Vol. 41...
- Wang, K.L. (2025a), “New perspective to the coupled fractional nonlinear Schrodinger equations in dual-core optical fibers”, Fractals, Vol....
- Wang, K.L. (2025b), “New dynamical behaviors and soliton solutions of the coupled nonlinear Schrödinger equation”, International Journal of...
- Wang, K.J., Wang, G.D. and Shi, F. (2023), “The pulse narrowing nonlinear transmission lines model within the local fractional calculus on...
- Wang, K.J., Liu, X.L., Wang, W.D., Li, S. and Zhu, H.W. (2025a), “Novel singular and non-singular complexiton, interaction wave and the complex...
- Wang, K.J., Zhu, H.W., Li, S., Shi, F., Li, G. and Liu, X.L. (2025b), “Bifurcation analysis, chaotic behaviors, variational principle, Hamiltonian...
- Wang, K.J., Zhu, H.W., Shi, F., Liu, X.L., Wang, G.D. and Li, G. (2025c), “Lump wave, breather wave and other abundant wave solutions to the...
- Yang, D.Y., Tian, B., Wang, M., Zhao, X., Shan, W.R. and Jiang, Y. (2022), “Lax pair, Darboux transformation, breathers and rogue waves of...
- Younas, U., Younis, M., Seadawy, A.R., Rizvi, S.T.R., Althobaiti, S. and Sayed, S. (2021), “Diverse exact solutions for modified nonlinear...
- Zaman, U.H.M., Arefin, M.A., Akbar, M.A. and Uddin, M.H. (2023), “Utilizing the extended tanh-function technique to scrutinize fractional...
- Zayed, E.M.E. and Alurrfi, K.A.E. (2015), “A new Jacobi elliptic function expansion method for solving a nonlinear PDE describing the nonlinear...
- Zayed, E.M., Alngar, M.E., El-Horbaty, M.M., Biswas, A., Kara, A.H., Yıldırım, Y. and Belic, M.R. (2021), “Cubic–quartic polarized optical...
