{"title":"哈密顿动力学中具有分岔和混沌的输电线路模型的解结构","authors":"Jian-ming Qi, Q. Cui, Le Zhang, Yiqun Sun","doi":"10.1142/s0218127423501080","DOIUrl":null,"url":null,"abstract":"Employing the Riccati–Bernoulli sub-ODE method (RBSM) and improved Weierstrass elliptic function method, we handle the proposed [Formula: see text]-dimensional nonlinear fractional electrical transmission line equation (NFETLE) system in this paper. An infinite sequence of solutions and Weierstrass elliptic function solutions may be obtained through solving the NFETLE. These new exact and solitary wave solutions are derived in the forms of trigonometric function, Weierstrass elliptic function and hyperbolic function. The graphs of soliton solutions of the NFETLE describe the dynamics of the solutions in the figures. We also discuss elaborately the effects of fraction and arbitrary parameters on a part of obtained soliton solutions which are presented graphically. Moreover, we also draw meaningful conclusions via a comparison of our partially explored areas with other different fractional derivatives. From our perspectives, by rewriting the equation as Hamiltonian system, we study the phase portrait and bifurcation of the system about NFETLE and we also for the first time discuss sensitivity of the system and chaotic behaviors. To our best knowledge, we discover a variety of new solutions that have not been reported in existing articles [Formula: see text], [Formula: see text]. The most important thing is that there are iterative ideas in finding the solution process, which have not been seen before from relevant articles such as [Tala-Tebue et al., 2014; Fendzi-Donfack et al., 2018; Ashraf et al., 2022; Ndzana et al., 2022; Halidou et al., 2022] in seeking for exact solutions about NFETLE.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. 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These new exact and solitary wave solutions are derived in the forms of trigonometric function, Weierstrass elliptic function and hyperbolic function. The graphs of soliton solutions of the NFETLE describe the dynamics of the solutions in the figures. We also discuss elaborately the effects of fraction and arbitrary parameters on a part of obtained soliton solutions which are presented graphically. Moreover, we also draw meaningful conclusions via a comparison of our partially explored areas with other different fractional derivatives. From our perspectives, by rewriting the equation as Hamiltonian system, we study the phase portrait and bifurcation of the system about NFETLE and we also for the first time discuss sensitivity of the system and chaotic behaviors. To our best knowledge, we discover a variety of new solutions that have not been reported in existing articles [Formula: see text], [Formula: see text]. 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引用次数: 0
摘要
本文采用riccti - bernoulli子ode方法(RBSM)和改进的Weierstrass椭圆函数方法,处理了所提出的[公式:见文]-维非线性分数阶输电线方程(NFETLE)系统。通过求解NFETLE可以得到无穷级数的解和weerstrass椭圆函数解。这些新的精确和孤立波解分别以三角函数、weerstrass椭圆函数和双曲函数的形式导出。NFETLE的孤子解的图形描述了图中解的动力学。我们还详细讨论了分数和任意参数对得到的部分孤子解的影响。此外,我们还通过比较我们部分探索的领域与其他不同的分数导数得出有意义的结论。从我们的角度出发,通过将方程改写为哈密顿系统,我们研究了NFETLE系统的相画像和分岔,并首次讨论了系统的灵敏度和混沌行为。据我们所知,我们发现了现有文章中没有报道的各种新的解决方案[公式:见文本],[公式:见文本]。最重要的是,在寻找解决方案的过程中有迭代的想法,这在之前的相关文章中没有见过,如[Tala-Tebue et al., 2014;Fendzi-Donfack et al., 2018;Ashraf et al., 2022;Ndzana et al., 2022;Halidou et al., 2022]寻求NFETLE的精确解。
Solution Structures of an Electrical Transmission Line Model with Bifurcation and Chaos in Hamiltonian Dynamics
Employing the Riccati–Bernoulli sub-ODE method (RBSM) and improved Weierstrass elliptic function method, we handle the proposed [Formula: see text]-dimensional nonlinear fractional electrical transmission line equation (NFETLE) system in this paper. An infinite sequence of solutions and Weierstrass elliptic function solutions may be obtained through solving the NFETLE. These new exact and solitary wave solutions are derived in the forms of trigonometric function, Weierstrass elliptic function and hyperbolic function. The graphs of soliton solutions of the NFETLE describe the dynamics of the solutions in the figures. We also discuss elaborately the effects of fraction and arbitrary parameters on a part of obtained soliton solutions which are presented graphically. Moreover, we also draw meaningful conclusions via a comparison of our partially explored areas with other different fractional derivatives. From our perspectives, by rewriting the equation as Hamiltonian system, we study the phase portrait and bifurcation of the system about NFETLE and we also for the first time discuss sensitivity of the system and chaotic behaviors. To our best knowledge, we discover a variety of new solutions that have not been reported in existing articles [Formula: see text], [Formula: see text]. The most important thing is that there are iterative ideas in finding the solution process, which have not been seen before from relevant articles such as [Tala-Tebue et al., 2014; Fendzi-Donfack et al., 2018; Ashraf et al., 2022; Ndzana et al., 2022; Halidou et al., 2022] in seeking for exact solutions about NFETLE.