We have solved the Burgers-Fisher (BF) type equations, with time-dependent coefficients of convection and reaction terms, by using the auxiliary equation method. A class of solitary wave solutions are obtained, and some of which are derived for the first time. We have studied the effect of variable coefficients on physical parameters (amplitude and velocity) of solitary wave solutions. In some ...

this paper presents discrete galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. we use the generalized jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. numerical results are presented to demonstrate the effectiven...

Solitary wave solutions to the Broer-Kaup equations and approximate long water wave equations are considered challenging by using the rst integral method.The exact solutions obtained during the present investigation are new. This method can be applied to nonintegrable equations as well as to integrable ones.

Typically, many of the modern buildings have concrete walls constructed from cinder block walls, that have periodic nature in their relative dielectric constant. This periodic nature excites higher-order Floquet harmonic modes at microwave frequencies, which leads to the propagation of scattered waves along with non-specular directions. Periodic structures exhibit different behaviors when illum...

and Applied Analysis 3 3. An Analysis of the Methods The following is given nonlinear partial differential equations (BBM and KdV equations) with two variables x and t as F (u, u t , u x , u xx , u xxx ) = 0 (15) can be converted to ordinary deferential equations: F (u, u 󸀠 , u 󸀠󸀠 , u 󸀠󸀠󸀠 ) = 0, (16) by using a wave variable ξ = x−ct. The equation is integrated as all terms contain derivatives ...