This paper studies the phi-four equation that arises in Quantum Mechanics. The topological 1-soliton solution or kink solution is obtained by the ansatz method. The bifurcation analysis is then subsequently carried out and several other solutions are retrieved from the analysis. These solutions include the solitary wave solutions, periodic waves and periodic singular waves. The constraint condi...

    M. and M.   Abstract: Existence and uniqueness of solution for singular 2-D systems depends on regularity condition. Simple regularity implies regularity and under this assumption, the generalized wave model (GWM) is introduced to cast singular 2-D system of equations as a family of non-singular 1-D models with variable structure.These index dependent models, along with a set of boundary co...

We consider a di erential equation describing the mass balance in a soil hydrology model with noninvertible Preisach-type hysteresis. We approximate the singular Preisach operator by regular ones and show, as main result, that the solutions of the regularized problem converge to a solution of the original one as the regularization parameter tends to zero. For monotone right hand sides, we prove...

We study a singularly perturbed system of partial differential equations that models a one-dimensional array of coupled Chua’s circuits. The PDE system is a natural generalization to the FitzHugh-Nagumo equation. In part I of the paper, we show that similar to the FitzHugh-Nagumo equation, the system has periodic traveling wave solutions formed alternatively by fast and slow flows. First, asymp...

The theory of phase resetting can reveal important information about the dynamic behavior of a periodic system when a single brief stimulus is applied to that system at the appropriate time. Phase resetting studies have revealed the existence in some biological systems of a vulnerable stimulus window generating desynchronization and suppression of the activity. The objective of this study was t...

In this paper, a numerical method for solving the constrained optimal control of time-varying singular systems with quadratic performance index is presented. Presented method is based on Bernste in polynomials. Operational matrices of integration, differentiation and product are introduced and utilized to reduce the optimal control of time-varying singular problems to the solution of algebraic ...

In the paper, a auxiliary equation expansion method and its a lgorithm is proposed by studying a second order nonlinear ordinary differential equation with a six-degree term.The method is applied to the generalized derivative Schrödinger equation .As a result,some new exact traveling wave solution are obtained which singular solutions,triangular periodic wave solution and Jacobian elliptic func...

Our purpose in this paper is to extend p{cyclic SOR theory to consistent singular systems and to apply the results to the solution of large scale systems arising, e.g., in queueing network problems in Markov analysis. Markov chains and queueing models lead to structured singular linear systems and are playing an increasing role in the understanding of complex phenomena arising in computer, comm...

Numerically reliable algorithms to compute the periodic non-negative definite stabilizing solutions of the periodic differential Riccati equation (PRDE) and discrete-time periodic Riccati equation (DPRE) are proposed. For the numerical solution of PRDEs, a new multiple shooting-type algorithm is developed to compute the periodic solutions in an arbitrary number of time moments within one period...