51. Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
- Author
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Bilal Muhammad, Iqbal Javed, Ali Rashid, Awwad Fuad A., and Ismail Emad A. A.
- Subjects
fractional partial differential equations ,homogenous balancing principle ,modified extended direct algebraic method ,wave transformation ,breather waves ,generalized riccati node ,Physics ,QC1-999 - Abstract
This article develops and investigates the behavior of soliton solutions for the spatiotemporal conformable Klein–Gordon equation (CKGE), a well-known mathematical physics model that accounts for spinless pion and de-Broglie waves. To accomplish this task, we deploy an effective analytical method, namely, the modified extended direct algebraic method (mEDAM). This method first develops a nonlinear ordinary differential equation (NODE) through the use of a wave transformation. With the help of generalized Riccati NODE and balancing nonlinearity with the highest derivative term, it then assumes a finite series-form solution for the resulting NODE, from which four clusters of soliton solutions – generalized rational, trigonometric, exponential, and hyperbolic functions – are derived. Using contour and three-dimensional visuals, the behaviors of the soliton solutions – which are prominently described as dark kink, bright kink, breather, and other NN-soliton waves – are examined and analyzed. These results have applications in solid-state physics, nonlinear optics, quantum field theory, and a more thorough knowledge of the dynamics of the CKGE.
- Published
- 2024
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