Introduction: Solitary fibrous tumor is a rare, mesenchymal neoplasm that has been reported in numerous sites. Occurrence in the parotid gland is exceedingly rare.   Case Report: A 53-year-old man with a 2 cm solitary fibrous tumor of the left parotid gland, that was observed clinically and operatively and thought to be a neoplasm arising from Stensen's duct, is described. A pre-operative CT sc...

Huxley equation is a core mathematical framework for modern biophysically based neural modeling. It is often useful to obtain a generalized solitary solution for fully understanding its physical meanings. There are many methods to solve the equation, but each method can only lead to a special solution. This paper suggests a relatively new method called the Exp-function method for this purpose. ...

In this paper, we apply He’s semi-inverse method to establish a variational theory for the Boussinesq system. Based on this formulation, a solitary solution can be easily obtained using Ritz method. Moreover, the results are also compared with He’s homotopy perturbation method, Liao’s homotopy analysis method and homotopy padémethod. The results reveal that the proposed method is very effective...

We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa–Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, we establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from H1(R). In particular, the supersonic solitary shock w...

This paper focuses on applying the GDTM-Padé technique to solve the non-linear differential-difference equation. The bell-shaped solitary wave solution of Belov-Chaltikian lattice equation is considered. Comparison between the approximate solutions and the exact ones shows that this technique is an efficient and attractive method for solving the differential-difference equations.

Consider the focusing mass-critical nonlinear Hartree equation iut + u=−(| · |−2 ∗ |u|2)u for spherically symmetric H 1 x initial data with ground state mass M(Q) in dimension d 5. We show that any global solution u which does not scatter must be the solitary wave eitQ up to phase rotation and scaling. © 2008 Elsevier Inc. All rights reserved. MSC: 35Q55

In this article, some fresh solitary and periodic solutions of the Gardner equation have been explored with free parameters via the Exp -function method. The solutions are presented in terms of hyperbolic and trigonometric functions. The solutions and are revealed in figures. The symbolic computation software, such as, Maple 13, make the solution procedure straightforward and concise. AMS subje...

Abstract In this study, we present two different methods a sech-tanh method and extended tanh-method to obtained the soliton solutions of the two-dimensional Korteweg-de Vries-Burgers (KdVB) equation with the initial conditions. These solutions include bright and dark solitary wave solutions, triangular solutions and complex line soliton wave solution. These solutions are stable and have applic...