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Generation and propagation of acoustic solitons in a periodic waveguide of air-water metamaterials
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Extended shallow water wave equations are derived, using the method of asymptotic expansions, from the Euler (or water wave) equations. These extended models are valid one order beyond the usual weakly nonlinear, long wave approximation, incorporating all appropriate dispersive and nonlinear terms. Specifically, first we derive the extended Korteweg–de Vries (KdV) equation, and then proceed with the extended Benjamin–Bona–Mahony and the extended Camassa–Holm equations in (1+1)-dimensions, the extended cylindrical KdV equation in the quasi-one dimensional setting, as well as the extended Kadomtsev–Petviashvili and its cylindrical counterpart in (2+1)-dimensions. We conclude with the case of the extended Green–Naghdi equations.
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The investigation of Electron-Positron-Ion (EPI) plasma? ?a fully ionised gas of electrons and positrons that includes astrophysical plasmas like solar winds? ?has attracted a great deal of attention over the last twenty years. A new study published in
EPJ D by Garston Tiofack, Faculty of Sciences, University of Marousa, Cameroon, and colleagues, assesses the dynamics of positron acoustic waves (PAWS) in EPI plasmas whilst under the influence of magnetic fields, or magnetoplasmas.
The authors studied the changes in PAWs using a framework of Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations finding a former led to compressive positron acoustic solitary waves (PASWs), whilst the latter resulted in the same and additional rarefactive PASWs. Mathematical models and numerical simulations performed by the researchers also allowed them to consider the effect of various other factors on the magnetoplasma including the concentration of hot electrons to that