Riccati equation

About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.

Conditional similarity reduction approach: Jimbo-Miwa equation

Abstract: The direct method developed by Clarkson and Kruskal (1989 J. Math. Phys. 30 2201) for finding the symmetry reductions of a nonlinear system is extended to find the conditional similarity solutions. Using the method of the Jimbo-Miwa (JM) equation, we find that three well-known (2+1)-dimensional models - the asymmetric Nizhnik-Novikov-Veselov equation, the breaking soliton equation and the Kadomtsev-Petviashvili equation - can all be obtained as the conditional similarity reductions of the JM equation.

Applications of three methods for obtaining optical soliton solutions for the Lakshmanan–Porsezian–Daniel model with Kerr law nonlinearity

Abstract: This paper examines new travelling wave solutions to the Lakshmanan–Porsezian–Daniel (LPD) model with Kerr nonlinearity using Backlund transformation method based on Riccati equation, Kudryashov method and a new auxiliary ordinary differential equation (ODE). The three methods are adequately utilised, and some new rational-type hyperbolic and trigonometric function solutions are derived in different shapes for the aforementioned model. We confirm that our methods are more efficient than the other methods and it might be used in many other such types of nonlinear equations arising in the basic fabric of communications network technology and nonlinear optics.

Soliton solutions, Liouville integrability and gauge equivalence of Sasa Satsuma equation

Abstract: Exact integrability of the Sasa Satsuma eqation (SSE) in the Liouville sense is established by showing the existence of an infinite set of conservation laws. The explicit form of the conserved quantities in term of the fields are obtained by solving the Riccati equation for the associated 3x3 Lax operator. The soliton solutions in particular, one and two soliton solutions, are constructed by the Hirota's bilinear method. The one soliton solutions is also compared with that found through the inverse scattering method. The gauge equivalence of the SSE with a generalized Landau Lifshitz equation is established with the explicit construction o

Optimal control of large space structures using distributed gyricity

Abstract: An optimal formulation is developed for the shape control of large flexible spacecraft possessing a distribution of control moment gyros. The structure is modeled as a continuum in mass, stiffness, and gyricity (stored angular momentum). A small, linear viscous damping term completes the dynamical description. The equation of motion is formulated in continuum form, and a brief eigenanalysis is presented that permits the modal equations of motion to be derived. The optimal control problem is treated using distributed-parameter concepts, and a modal expansion for the resulting Riccati operator reduces the problem to the solution of a matrix Riccati equation. Such an approach permits pointwise control moment gyros as well as the distributed analog to be handled with the same theory. By means of an example, the use of distributed gyricity is demonstrated to be very effective for shape control of large space structures. Moreover, the notion of a continuous distribution of gyricity is shown to be beneficial in modeling the dynamics and control of flexible spacecraft employing many control moment gyros.