In this paper, we construct a Darboux transformation and the related Backlund for super-symmetric Sawada-Kotera (SSK) equation. The associated nonlinear superposition formula is ...

Abstract: In this paper, through a new transformation, the combined KdvBurgers equation with variable coefficients(vcKdvB) is reduced to a new simplified equation.Based on the homogeneous balance principle(HBP),we studied the Backlund transformation(BT) and several exact soliton-like solutions to this vcKdvB equation. Including single kink-like solitary wave solutions, double-soliton-like solut...

Abstract—In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. N...

Based on symbolic manipulation program Maple and using Riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient Broer-Kaup system in quite a straightforward manner. The known solutions of Riccati equation are used to construct new solutions for variable coefficient Broer...

first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...

based on symbolic manipulation program maple and using riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient broer--kaup system in quite a straightforward manner. the known solutions of riccati equation are used to construct new solutions for variable coefficient broe...

Abstract—In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be ...

This paper suggests a closed-form solution of particular case of an algebraic Riccati equation and its application example to optimal and smooth motion planning for a given linear quadratic performance index. Actually, the algebraic Riccati equation can be changed into Moser-Veselov equation by deriving both symmetric and skew-symmetric conditions from an algebraic Riccati equation itself. Also...

some preliminaries about the integrable families of riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional schrodinger equation with the kerr law nonlinearity. finally by using of this method and solutions of ri...