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

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 includin...

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Bibliographic Details
Published in:Pramāṇa 2024-08, Vol.98 (3), Article 124
Main Authors: Liu, Bo, Duan, Zhou-Bo, Niu, Li-Fang
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Astroparticles
Asymmetry
Elliptic functions
Event horizon
Exact solutions
Exponential functions
Hyperbolic functions
Mathematical analysis
Nonlinear differential equations
Observations and Techniques
Parameters
Parametric amplifiers
Partial differential equations
Physics
Physics and Astronomy
Solitary waves
Superconductivity
Transmission lines
Traveling waves
Trigonometric functions
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Summary: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.
ISSN:0973-7111
0304-4289
0973-7111
DOI:10.1007/s12043-024-02791-6