In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied tho...In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.展开更多
In the realm of nonlinear physics, it is crucial to establish precise traveling wave solutions and solitary wave solutions for a variety of nonlinear models, as this aids our exploration of these fields. In this paper...In the realm of nonlinear physics, it is crucial to establish precise traveling wave solutions and solitary wave solutions for a variety of nonlinear models, as this aids our exploration of these fields. In this paper, we propose a new method to construct precise solitary wave solutions if nonlinear equation with complex structure. As an application, we employ this method to solve the Burgers-Fisher equation, yielding a multitude of new solitary wave solutions. This approach demonstrates a broader applicability in addressing nonlinear evolution equations (NLEEs).展开更多
文摘In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.
文摘In the realm of nonlinear physics, it is crucial to establish precise traveling wave solutions and solitary wave solutions for a variety of nonlinear models, as this aids our exploration of these fields. In this paper, we propose a new method to construct precise solitary wave solutions if nonlinear equation with complex structure. As an application, we employ this method to solve the Burgers-Fisher equation, yielding a multitude of new solitary wave solutions. This approach demonstrates a broader applicability in addressing nonlinear evolution equations (NLEEs).
