The quadratic matrix equation AX2 + B X +C = 0 in n ×n matrices arises in applications and is of intrinsic interest as one of the simplest nonlinear matrix equations. We give a complete characterization of solutions in terms of the generalized Schur decomposition and describe and compare various numerical solution techniques. In particular, we give a thorough treatment of functional iteration m...

A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear differential equations have exact solutions which are general solution of the simplest integrable e...

In this paper we study the coupled integrable dispersionless system (CIDS), which arises in the analysis of several problems in applied mathematics and physics. Lie symmetry analysis is performed on CIDS and symmetry reductions and exact solutions with the aid of simplest equation method are obtained. In addition, the conservation laws of the CIDS are also derived using the multiplier (and homo...

A direct approach to calculating the hypersingular integral for a threedimensional Galerkin approximation is presented. The method does not employ either Stokes' Theorem or a regularization process to transform the integrand before the evaluation is carried out. Integrating two of the four dimensions analytically, the potentially divergent terms arising from the coincident and adjacent edge int...

Abstract A new three dimensional nonlinear dynamic theoretical model is derived from fluid mechanics system. In this paper, From the quasi-geostrophic barotropic potential vorticity equation, we obtain a dissipative Boussinesq equation by reduced perturbation method, i.e. u tt + e 1 xx 2 ( ) 3 txy 4 xxxx 5 xxyy = 0 . It emphasized that different existing equations, which describe Rossby waves i...

We have established a new dynamical model of microtubules based on their intrinsic dipolar character. The model assumes a single angular degree of freedom per dimer describing the conformational displacements of constituent dimers in radial direction. A corresponding nonlinear dynamical equation of motion is solved both analytically, using the simplest equation method, and numerically. It is sh...

Experimental studies of one-nucleon knockout from magic nuclei suggest that their nucleon orbits are not fully occupied. This conflicts a commonly accepted view of the shell closure associated with such nuclei. The conflict can be reconciled if the overlap between initial and final nuclear states in a knockout reaction are calculated by a nonstandard method. The method employs an inhomogeneous ...