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Journal of Function Spaces, 2022 We mainly discuss the relevant properties of the solution of the Riccati equation in this paper. By virtue of our previous derivation, we will give several uniqueness conclusions that the initial value problems of some kinds of the Riccati equation with ...
Shi-you Lin, Li-sha Chen, Bo-yang Li
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Riccati equation perspective on Landau-Zener transitions
Physical Review ResearchWe express the dynamics of the two probability amplitudes in the elementary Landau-Zener problem in terms of the solution of the corresponding Riccati differential equation and identify three key features: (i) The solution of the Riccati equation ...
Eric P. Glasbrenner +3 more
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Boundary Value Problems, 2010 We used what we called extended Fan's sub-equation method and a new compound Riccati equations rational expansion method to construct the exact travelling wave solutions of the Davey-Stewartson (DS) equations.
Hassan Zedan
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The development of the deterministic nonlinear PDEs in particle physics to stochastic case
Results in Physics, 2018 In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation.
Mahmoud A.E. Abdelrahman, M.A. Sohaly
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On the matrix riccati equation
Information Sciences, 1971 Properties of the algebraic equation A^TX+XA-XBQ"2^-^1B^TX+Q"1=0 are studied for arbitrary nonnegative definite and positive definite matrices Q"1 and Q"2. The results are used to study the possible number of stationary solutions of the Riccati equation.
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Existance theroms for the matrix Riccati equation W′+WP(t)W+Q(t)=0
International Journal of Mathematics and Mathematical Sciences, 1978 Sufficient conditions are established for the matrix Riccati equation to have a symmetric solution on a given interval. The criteria involve integral conditions on the coefficient matrices of the Riccati equation.
Robert A. Jones
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Planar nonautonomous polynomial equations: The Riccati equation
Journal of Differential Equations, 2008 The problem on the existence of \(T\)-periodic solutions of Riccati equations of the form \[ \dot z=a(t)z^2+b(t)z+c(t) \] in the complex plane, where \(a\), \(b\), and \(c\) are \(T\)-periodic, is considered. The main theorems present results on the existence of two such solutions.
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Advances in Mathematical Physics, 2013 A new method with a different auxiliary equation from the Riccati equation is used for constructing exact travelling wave solutions of nonlinear partial differential equations.
Bülent Kiliç, Hasan Bulut
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Upper bounds on the solution of coupled algebraic riccati equation
Journal of Inequalities and Applications, 2001 Upper bounds for eigenvalues of a solution to continuous time coupled algebraic Riccati equation (CCARE) and discrete time coupled algebraic Riccati equation (DCARE) are developed as special cases of bounds for the unified coupled algebraic Riccati ...
Czornik Adam, Świerniak Andrzej
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Oscillation criteria for perturbed half-linear differential equations
Electronic Journal of Qualitative Theory of Differential EquationsOscillatory properties of perturbed half-linear differential equations are investigated. We make use of the modified Riccati technique. A certain linear differential equation associated with the modified Riccati equation plays an important part. Improved
Manabu Naito
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