Search for interactions of phenomena described by the coupled Higgs field equation through analytical solutions
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Search for interactions of phenomena described by the coupled Higgs field equation through analytical solutions Md. Ekramul Islam1 · Hemonta Kumar Barman2 · M. Ali Akbar2 Received: 15 July 2020 / Accepted: 3 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The coupled Higgs field equation is significant for describing a system of conserved scalar nucleons interacting with the neutral scalar meson. The improved Bernoulli sub-equation function method and the sine–Gordon expansion method have been put in used in the current article, to interpret the dynamism of the particles through analytical solutions modelled by the coupled Higgs field equation. The interaction among the electrons and mesons has been found out and it is observed that the particle moves along the smooth path from one state to another. It is also vital to mark that the wave profile of the waves are velocity dependent and the incident is shown in the figures. Different types of soliton shape like, bell shape soliton, kink soliton, consolidated bell shape; anti-bell shape soliton, compacton, singular soliton, flat kink soliton etc. are ascertained by assigning individual quantities of the unidentified parameters whose propagations are portrayed in 3D and 2D surfaces. The solutions established in this study are further comprehensive, broad–ranging and some are new which have not been found in earlier research. The executed schemes are effective, compatible to computer algebra and deliver ample wide–ranging wave solutions. Keywords The coupled higgs field equation · The improved bernoulli sub-equation function method · The sine–gordon expansion method · Nonlinear evolution equations (NLEEs) · Soliton solutions
1 Introduction The NLEEs are the outstanding type of partial differential equations (PDEs) which were the focus of all embracing studies in different nonlinear science and engineering branches. A special class of exact solutions, namely the solitary wave solutions has scores of importance, since most of the physical incidents that arise in mathematical physics, technology and engineering fields are modeled by NLEEs. This type of waves is identified as the * M. Ali Akbar [email protected] 1
Department of Mathematics, Pabna University of Science and Technology, Pabna, Bangladesh
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Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
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soliton-like solutions to NLEEs that explain the wave process in dissipative and dispersive media. It gives a single soliton solution. But when several types of soliton arise in a solution they are defined as a soliton. The soliton concept plays a key role in different applied fields such as preformation of cluster in hydrodynamic models, the inertial fusion, the fission of liquid drops, the super deformed nuclei etc. However, the exact solutions to the NLEEs are frequently used to describe much physical significance, especially in plasma physics, fluid dynamics, meteorology,
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