The extended tanh-function expansion method for finding solutions to nonlinear evolution equations delivers solutions in a straightforward manner and in a neat and helpful form. On the other hand, the more recent but less efficient (G/G)-expansion method delivers solutions in a rather cumbersome form. It is shown that these solutions are merely disguised forms of the solutions given by the earl...

Heterotic supergravity with (1+3)–dimensional domain wall configurations and (warped) internal, six dimensional, almost-Kähler manifolds X are studied. Considering on ten dimensional spacetime, nonholonomic distributions with conventional double fibrations, 2+2+...=2+2+3+3, and associated SU(3) structures on internal space, we generalize for real, internal, almost symplectic gravitational struc...

Let us assume we are given an almost Poincaré, hyper-Thompson–Germain, compactly empty ring Σ′. It has long been known that tanh (X − |J |) ≤ ∫ inf uΞ,J→1 r dvΓ × · · ·+−∞k̃

In this paper, we have exploited the first-order sliding mode control method to track the ECG data of the human heart by three different nonlinear control laws. In order to lessen the intrinsic chattering of the classic sliding mode control system, smooth function approximations of the control input, by means of the hyperbolic tangent and the saturation function, were used. The fast Fourier tra...

The present paper aims to investigate the coupled nonlinear Schrödinger equation in magneto-optic waveguides having anti-cubic (AC) law nonlinearity. solitons secured with AC nonlinearity are extremely useful fiber-optic transmission technology. Three constructive techniques, namely, $$(G^{\prime }/G)$$ -expansion method, modified simple and extended tanh method utilized find exact soliton solu...

The reverse space-time nonlocal complex modified Kortewewg–de Vries (mKdV) equation is investigated by using the consistent tanh expansion (CTE) method. According to CTE method, a nonauto-Bäcklund transformation theorem of mKdV obtained. interactions between one kink soliton and other different nonlinear excitations are constructed via theorem. By selecting cnoidal periodic waves, interaction w...

also known as the diffusion equation, describes in typical applications of the evolution in time of the density u u x, t of some quantities such as heat and chemical concentration 1, page 44 . In this case, the thermal diffusivity and thermal conductivity of the medium are assumed to be constant. However, in some media such as gases, the parameters are proportional to the temperature of the med...

Our paper studies the optical solitons for Kundu–Eckhaus (KE) equation with quintic nonlinearity and Raman effect. By applying improved modified extended tanh-function method, many soliton solutions can be obtained such as bright solutions, dark singular solution. In addition, we obtain various types of namely, periodic exponential rational Jacobi elliptic Weierstrass doubly solutions. Moreover...

We consider the problem of the evolution of the fine structure coefficient α under the assumption that the scalar field coupling to the Maxwell term satisfies the condition mt ≫ 1 for coherent dark matter oscillations. In this case we find that the coupling scale f in the leading order coupling −(φ/4f)FμνF μν affects the cosmological evolution of α according to ln(α/α0) ∝ ξ(mPl/f)× ln(tanh(t/2τ...