High-precision observational data have confirmed with startling evidence that the Universe is currently undergoing a phase of accelerated expansion. This phase, one of the most important and challenging current problems in cosmology, represents a new imbalance in the governing gravitational equations. Historically, physics has addressed such imbalances by either identifying sources that were pr...

Abstract The accelerated expansion of the universe demands presence an exotic matter, namely dark energy. Though cosmological constant fits this role very well, a scalar field minimally coupled to gravity, or quintessence, can also be considered as viable alternative for constant. We study f ( R ) gravity models which lead effective description energy implemented by quintessence fields in Einst...

The conventional Fourier coefficient asymptotic expansion is derived by means of a specific contour integration. An adjusted expansion is obtained by deforming this contour. A corresponding adjustment to the Euler-Maclaurin expansion exists. The effect of this adjustment in the error functional for a general quadrature rule is investigated. It is the same as the effect of subtracting out a pair...

The nonlinear equations of mathematical physics are major subjects in physical science [1]. Recently many new approaches for finding the exact solutions to nonlinear wave equations have been proposed, for example, tanh-sech method [2–4], extended tanh method [5–7], sine-cosine method [8–10], homogeneous balance method [11, 12], Jacobi elliptic function method [13–16], F -expansion method [17–19...

Some new generalized solitary solutions of the Klein–Gordon–Schrödinger equations are obtained using the Exp-function method, which include some known solutions obtained by the F-expansion method and the homogeneous balance method in the open literature as special cases. It is shown that the Exp-function method is a straight, concise, reliable and promising mathematical tool for solving nonline...

In this article, we give the extended trial equation method for solving nonlinear partial differential equations with higher order nonlinearity. By use of this method, the exact travel-ing wave solutions including soliton solution, singular soliton solutions, rational function solution and elliptic integral function solution to one-dimensional general improved KdV (GIKdV) equation and Rðm; nÞ e...