Soliton solutions of the TWPA-SNAIL transmission line circuit equation under continuum approximation via the Jacobi elliptic function expansion method

IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pramana Pub Date : 2024-08-28 DOI:10.1007/s12043-024-02791-6
Bo Liu, Zhou-Bo Duan, Li-Fang Niu
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Abstract

In this paper, we study the travelling wave parametric amplifier-superconducting nonlinear asymmetric inductive element (TWPA-SNAIL) transmission line circuit equation and its variable coefficients form, which may describe transmission line circuits for travelling wave parametric amplifiers including superconducting nonlinear asymmetric inductive elements. We derive some exact solutions, including dark soliton, bright soliton, periodic, trigonometric function and hyperbolic function solutions using Jacobi elliptic function expansion method. The soliton solutions of this circuit equation are useful to analogue black–white hole event horizon pairs. To better describe the dynamical behaviour of these solutions, we plot three-dimensional density and two-dimensional images. By varying the parameters, we find that some parameters have an effect on the structure of the solution. In addition, for the variable coefficient equations, we present images containing trigonometric and exponential functions in the solution and obtain some satisfactory results by comparing the graphs with the coefficient functions. The results show that the Jacobi elliptic function expansion method is a remarkable, direct and desirable method for solving a class of nonlinear partial differential equations.

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通过雅可比椭圆函数展开法求解连续近似条件下的 TWPA-SNAIL 传输线电路方程的孤子解
本文研究了行波参数放大器-超导非线性非对称电感元件(TWPA-SNAIL)传输线电路方程及其可变系数形式,它可以描述包括超导非线性非对称电感元件在内的行波参数放大器的传输线电路。我们利用雅可比椭圆函数展开法推导出一些精确解,包括暗孤子解、亮孤子解、周期解、三角函数解和双曲函数解。该电路方程的孤子解有助于模拟黑白洞事件视界对。为了更好地描述这些解的动力学行为,我们绘制了三维密度和二维图像。通过改变参数,我们发现一些参数对解的结构有影响。此外,对于可变系数方程,我们给出了解中包含三角函数和指数函数的图像,并通过比较图形和系数函数获得了一些令人满意的结果。结果表明,雅可比椭圆函数展开法是求解一类非线性偏微分方程的显著、直接和理想的方法。
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来源期刊
Pramana
Pramana 物理-物理:综合
CiteScore
3.60
自引率
7.10%
发文量
206
审稿时长
3 months
期刊介绍: Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.
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