Abstract
This paper considers methods to extract exact, explicit, and new single soliton solutions related to the nonlinear Klein-Gordon-Schrödinger model that is utilized in the study of neutral scalar mesons associated with conserved scalar nucleons coupled through the Yukawa interaction. Three state of the art integration schemes, namely, the e−Φ(ξ)-expansion method, Kudryashov's method, and the tanh-coth expansion method are employed to extract bright soliton, dark soliton, periodic soliton, combo soliton, kink soliton, and singular soliton solutions. All the constructed solutions satisfy their existence criteria. It is shown that these methods are concise, straightforward, promising, and reliable mathematical tools to untangle the physical features of mathematical physics equations.
Highlights
Many of the problems arising in mathematically-oriented scientific fields such as physics and engineering are described by partial differential equations (PDEs)
The results presented in this piece of research could be very useful in discussing the physical properties of the different nonlinear evolution equations emerging in quantum mechanics, fluid dynamics, and plasma physics
It is important to clarify that the analytical methods utilized in this article are truly state of the art techniques for extracting the soliton solution of the non-linear Klein-Gordon-Schrödinger model
Summary
Many of the problems arising in mathematically-oriented scientific fields such as physics and engineering are described by partial differential equations (PDEs). PDEs are used to depict an ample variety of phenomena such as dislocations in crystals, superconductivity, laser pulses in two-phase [1, 2], waves in ferromagnetic materials, and many more [3,4,5,6]. Many theories such as electromagnetism, diffusion, fluid flow, etc. Exploring exact solutions for PDEs plays an important role in such fields These solutions might be essential and important for exploring some physical phenomena. Due to the invention of algebraic system solvers such as Mathematica and Maple, many integrating schemes have been proposed, such as the e− (ξ)-expansion method, Hirota’s bilinear method, the homogeneous balance reduction of the PDE to a quadrature problem, the truncated Painlevé expansion, etc. [9,10,11,12,13]
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