In the method presented here, the discrete sine method, the basis functions consist of sine functions defined on a set of parallel discretization lines. The method is a combination of a scalar version of the finite difference method and the sine method. The choice of the basis set leads, for the eigenvalue equation to be solved, to a sparse matrix with a small bandwidth. As a consequence, the p...

In this paper, we established traveling wave solutions of the nonlinear evolution equation. The sine-cosine method was used to construct travelling wave solutions of the Fitzhugh-Nagumo equation and Cahn-Allen equation. Graphical interpretation shows that obtained results include periodic and Soliton wave solutions. It is also shown that for α =−1, solutions of Fitzhugh-Nagumo equation coincide...

We present an analytic study of the finite size effects in Sine–Gordon model, based on the semiclassical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi–periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is ...

The conserved Sine-Gordon equation with nonconserved shot noise is used to model homoepitaxial crystal growth. With increasing coverage the renormalized pinning

Using the power series expansion technique, this paper established two new inequalities for sine function and tangent bounded by functions x2sin(λx)/(λx)α x2tan(μx)/(μx)β. These results are better than ones in previous literature.

a new derivation of the quantum boltzmann transport equation for the fermion system from the quantum time evolution equation for the wigner distribution function is presented. the method exhibits the origin of the time - irreversibility of the boltzmann equation. in the present work, the spin dependent and indistinguishibility of particles are also considered.

Spatiotemporal chaos arising from the competition between sine-Gordonbreather and kink-antikink-pair solitons by reshaping an ac force is demonstrated. After introducing soliton collective coordinates, Melnikov’s method is applied to the resulting effective equation of motion to estimate the parameterspace regions of the ac force where homoclinic bifurcations are induced. The analysis reveals t...

In this paper, a type of fully nonlinear Sine-Gordon equations and the approximate Sine-Gordon equation (under the condition: |up|is very small) are studied.Through proper transformation, some initial value problems of many equations with special nonlinear terms are solved by the Adomian decomposition method and some exact solutions: kink solution ,compacton solution, multi-compacton solution, ...