Screening $$\Lambda $$ in a new modified gravity model

We study a new model of Energy-Momentum Squared Gravity (EMSG), called Energy-Momentum Log Gravity (EMLG), constructed by the addition of the term $$f(T_{\mu \nu }T^{\mu \nu })=\alpha \ln (\lambda \,T_{\mu \nu }T^{\mu \nu })$$f(TμνTμν)=αln(λTμνTμν), envisaged as a correction, to the Einstein–Hilbert action with cosmological constant $$\Lambda $$Λ. The choice of this modification is made as a specific way of including new terms in the right-hand side of the Einstein field equations, resulting in constant effective inertial mass density and, importantly, leading to an explicit exact solution of the matter energy density in terms of redshift. We look for viable cosmologies, in particular, an extension of the standard $$\Lambda $$ΛCDM model. EMLG provides an effective dynamical dark energy passing below zero at large redshifts, accommodating a mechanism for screening $$\Lambda $$Λ in this region, in line with suggestions for alleviating some of the tensions that arise between observational data sets within the standard $$\Lambda $$ΛCDM model. We present a detailed theoretical investigation of the model and then constrain the free parameter $$\alpha '$$α′, a normalisation of $$\alpha $$α, using the latest observational data. The data does not rule out the $$\Lambda $$ΛCDM limit of our model ($$\alpha '= 0$$α′=0), but prefers slightly negative values of the EMLG model parameter ($$\alpha '= -0.032\pm 0.043$$α′=-0.032±0.043), which leads to the screening of $$\Lambda $$Λ. We also discuss how EMLG relaxes the persistent tension that appears in the measurements of $$H_0$$H0 within the standard $$\Lambda $$ΛCDM model.

Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky–Konopelchenko equation by geometric approach

In this paper, the symmetry analysis and similarity reduction of the (2[Formula: see text]+[Formula: see text]1)-dimensional Bogoyavlensky–Konopelchenko (B–K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2[Formula: see text]+[Formula: see text]1)-dimensional B–K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2[Formula: see text]+[Formula: see text]1)-dimensional B–K equation is obtained.

Variable separation for time fractional advection-dispersion equation with initial and boundary conditions

In this paper, variable separation method combined with the properties of Mittag-Leffler function is used to solve a variable-coefficient time fractional advection-dispersion equation with initial and boundary conditions. As a result, a explicit exact solution is obtained. It is shown that the variable separation method can provide a useful mathematical tool for solving the time fractional heat transfer equations.

Some Nonlinear, Equatorially Trapped, Nonhydrostatic Internal Geophysical Waves

The author presents an explicit exact solution to the governing equations for geophysical equatorial waves in the β-plane setting. The solution describes equatorially trapped waves propagating eastward above the thermocline and beneath the near-surface layer where wind effects are confined. At great depths the water is still, while the transition toward the large-amplitude oscillation of the thermocline is accommodated by an eastward-flowing current. Above the thermocline a flow reversal occurs, with the underlying current flowing westward close to the layer where wind effects are confined.

EXACT SOLITARY-WAVE SOLUTIONS FOR THE NONLINEAR DISPERSIVE K(2,2,1) and K(3,3,1) EQUATIONS BY THE HOMOTOPY PERTURBATION METHOD

We implemented homotopy perturbation method for approximating the solution to the nonlinear dispersive K(m,n,1) type equations. By using this scheme, the explicit exact solution is calculated in the form of a quickly convergent series with easily computable components. To illustrate the application of this method, numerical results are derived by using the calculated components of the homotopy perturbation series.

Forced Motion of Elastic Plates

A general method is presented for the solution of dynamic boundary-value problems of elastic plates subjected to time-dependent normal surface loads and/or time-dependent boundary conditions. As a demonstration of the method, an explicit, exact solution of the axisymmetric response of a ring plate is presented. The plate is clamped at the outer boundary and subjected to a suddenly applied transverse shear force which is uniformly distributed over the rotationally restrained inner boundary.