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...

A new type of variable coefficient Runge-Kutta-Nyström methods is proposed for solving the initial value problems of the special form y(t) = f(t, y(t)). The method is based on the exact integration of some given functions in order to solve the problem exactly when the solution is the linear combination of these functions. If this is not the case, the algebraic order (order of accuracy) of the m...

In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to Dynamical system in a new Double-Chain Model of DNA and a diffusive predator-prey system which play an important role in biology.

We construct a faithful interpretation of Lukasiewicz's logic in the product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable. We prove a completeness theorem for the product logic extended by a unary connective 4 of Baaz 1]. We show that GG odel's logic is a sublogic of this extended product logic. We also ...

In this study, a comparison of solutions for tracking data from the term project obtained by using two different overlapping sets of range and range rate data was completed. The original data file contained 385 points over a time period of 18,340 seconds, or approximately 5 hours. This data was divided into two parts with some overlapping data points. The first data set covered the time period ...

By using an extended ( ′ G )-expansion method, we construct the traveling wave solutions of the (2+1)dimensional Painleve integrable Burgers equations, the (2+1)-dimensional Nizhnik-Novikov-Veselov equations, the (2+1)-dimensional Boiti-Leon-Pempinelli equations and the (2+1)-dimensional dispersive long wave equations, where G satisfies the second order linear ordinary differential equation. By...