A new integrable two-component system with cubic nonlinearity

Model-Independent Adaptive Control of Chua's System with cubic Nonlinearity

This paper proposes a linear adaptive state feedback controller which achieves asymptotic tracking of the controlled cubic Chua’s system. The gain vector is tuned using an adaptation law derived using the Lyapunov stability theory. The aim is to design an adaptive controller that mimics a predetermined input–output linearizing controller known for its effective performance in output tracking. W...

Analysis of the Reliability of a Three-Component System with Two Repairmen

In this paper authors have considered a system having three units A, B1 and B2. A is controlled by a controller and B1 and B2 are independent. Two repairmen are involved in repair of the system. One of the repairmen (the first) is the foreman (boss) and the other an assistant (apprentice). Whenever any unit fails, repair is undertaken by boss. If the boss is busy in repairing and at the same ti...

A Lax Operator Hierarchy for the New Fifth Order Integrable System

We consider the Lax representation of the new two-component coupled integrable system recently discovered by the author. Connection of the hierarchy of infinitely many Lax pairs with each other is presented.

Explicit Integrable Systems on Two Dimensional Manifolds with a Cubic First Integral

A few years ago Selivanova gave an existence proof for some integrable models, in fact geodesic flows on two dimensional manifolds, with a cubic first integral. However the explicit form of these models hinged on the solution of a nonlinear third order ordinary differential equation which could not be obtained. We show that an appropriate choice of coordinates allows for integration and gives t...

Undercompressive Shocks for a System of Hyperbolic Conservation Laws with Cubic Nonlinearity