‎in this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear pdes in mathmatical physics; namely the one-‎dimensional modified complex ginzburg-landau equation by using the $ (g^{'}/g) $ expansion method‎, homogeneous balance method, extended f-expansion method‎. ‎by ‎using homogeneous balance principle and the extended f-expansion, more periodic wave solutions expres...

An experimental study of the upper and lower bow force limits for bowed violin strings is reported. A bowing machine was used to perform bow strokes with a real violin bow on steel D and E strings mounted on a rigid monochord and on a violin, respectively. Measurements were systematically performed for 24 values of bow force and 11 values of relative bow-bridge distance at four bow velocities (...

Motivated by the fact that the Green’s function for the Helmholtz equation in 2D space is the Hankel function, we modified the traditional ansatz of geometrical optics by replacing the exponential function with the Hankel function. With the new ansatz, the leading order amplitude in the asymptotic expansion captures the amplitude change of the solution more accurately than the traditional one i...

In this work an expression for the solution of the Helmholtz equation for wedge spaces is derived. Such propagation spaces represent scenarios for many acoustical problems where a free field assumption is not eligible. The proposed sound field model is derived from the general solution of the wave equation in cylindrical coordinates, using sets of orthonormal basis functions. The latter are mod...

In this article we present two numerical models for solving transient heat conduction problems. One is based on dual reciprocity method and Trefftz method (dubbed DRM-Trefftz), and the other is based on dual reciprocity method and fundamental solution (dubbed DRM-MFS). A time stepping method is used in handling the time variable to convert the problem into a set of inhomogeneous modified Helmho...

Numerical solution of the Helmholtz equation is a challenging computational task, particularly when the wave number is large. For two-dimensional problems, direct methods provide satisfactory solutions, but large three-dimensional problems become unmanageable. In this work, the block-parallel CARP-CG algorithm [Parallel Computing 36, 2010] is applied to the Helmholtz equation with large wave nu...

We introduce the generalized Helmholtz-Gauss (gHzG) beam and analyze its propagation through optical systems described by ABCD matrices with real and complex elements. The transverse mathematical structure of the gHzG beam is form invariant under paraxial transformations and reduces to those of ordinary HzG and modified HzG beams as special cases. We derive a closed-form expression for the frac...