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In this article, the bright, dark, and singular solitons are being constructed for nonlinear longitudinal wave equation with dispersion caused by transverse Poisson’s effect in a magneto-electro-elastic circular rod. The solitary wave ansatz is used to carry out these solutions. The constraint conditions, for the existence of the soliton solutions, are also listed. This article provides a lot of encouragement for the researchers in this era. [ABSTRACT FROM AUTHOR]

In this work, we establish exact solutions for (2 + 1)- and (3 + 1)-dimensional shallow water wave equations. The -expansion method is used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed in terms of hyperbolic functions, trigonometric functions and rational functions. This method presents a wider applicability for handling nonlinear wave equations. [ABSTRACT FROM AUTHOR]

Electromagnetic localization and the existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band—where the magnetic permeability µ(?) is positive and the dielectric permittivity Ƹ(?) is negative—is described by a nonlinear Klein–Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the role played by the nonlinear dispersive term on solitary wave stability is discussed. [ABSTRACT FROM AUTHOR]