One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument. Recently, two rather different and general, that is, type independent solution methods have been developed for very large classes of linear and nonlinear systems of PDEs with possibly associated initial and/or boundary conditions. One of them, [5], is using stan...

A low level image processing, for examples, image denoising and finding a local structure in an image, is one of essential processes in computer vision. The nonlinear structure tensor [1] based on an anisotropic nonlinear diffusion processes has shown its capability for presenting useful information of an image, such as homogeneous regions, edges, and corners. The diffusion process to obtain a ...

Simulating the propagation of 3D ultrasonic waves in a nonlinear medium is a demanding task. It requires the solution of time-dependent and nonlinear partial differential equations (PDEs). For such nonlinear PDEs, we have to use an implicit numerical method that is very CPUintensive. Parallel simulation is therefore essential for studying those ultrasonic waves with satisfactory accuracy. We pr...

In recent years, nonlinear phenomena play a crucial role in appliedmathematics and physics. Directly searching for exact solutions of nonlinear partial differential equations (PDEs) has become more and more attractive partly due to the availability of computer symbolic systems like Mathematica or Maple that allow us to perform some complicated and tedious algebraic calculation on a computer as ...

Contrary to widespread perception, there is ever since 1994 a unified , general type independent theory for the existence of solutions for very large classes of nonlinear systems of PDEs. This solution method is based on the Dedekind order completion of suitable spaces of piece-wise smooth functions on the Euclidean domains of definition of the respective PDEs. The method can also deal with ass...

In this paper, using the tanh-function method, we introduce a new approach to solitary wave solutions for solving nonlinear PDEs. The proposed method is based on adding integration constants to the resulting nonlinear ODEs from the nonlinear PDEs using the wave transformation. Also, we use a transformation related to those integration constants. Some examples are considered to find their exact ...

This paper develops amodified variational iterationmethod coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs).The approximate solutions of PDEs are calculated in the form of a serieswhose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wave...

We construct, for any given ` = 1 2 + N0, second-order nonlinear partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. This is done for a particular realization of the algebras obtained by coset construction and we employ the standard Lie point symmetry technique for the construction of PDEs. It is obs...