Negative Binomial States of the Radiation Field and their Excitations are Nonlinear Coherent States

We show that the well-known negative binomial states of the radiation field and their excitations are nonlinear coherent states. Excited nonlinear coherent state are still nonlinear coherent states with different nonlinear functions. We finally give exponential form of the nonlinear coherent states and remark that the binomial states are not nonlinear coherent states.Comment: 10 pages, no figure

An enhanced nodal gradient finite element for non-linear heat transfer analysis

The present work is devoted to the analysis of non-linear heat transfer problems using the recent development of consective-interpolation procedure. Approximation of temperature is enhanced by taking into account both the nodal values and their averaged nodal gradients, which results in an improved finite element model. The novel formulation possesses many desirable properties including higher accuracy and higher-order continuity, without any change of the total number of degrees of freedom. The non-linear heat transfer problems equation is linearized and iteratively solved by the Newton-Raphson scheme. To show the accuracy and efficiency of the proposed method, several numerical examples are hence considered and analyzed

MIMO nonlinear PID predictive controller

A class of nonlinear generalised predictive controllers (NGPC) is derived for multi-input multi-output (MIMO) nonlinear systems with offset or steady-state response error. The MIMO composite controller consists of an optimal NGPC and a nonlinear disturbance observer. The design of the nonlinear disturbance observer to estimate the offset is particularly simple, as is the associated proof of overall nonlinear closed-loop system stability. Moreover, the transient error response of the disturbance observer can be arbitrarily specified by simple design parameters. Very satisfactory performance of the proposed MIMO nonlinear predictive controller is demonstrated for a three-link nonlinear robotic manipulator example

Superposition of Elliptic Functions as Solutions For a Large Number of Nonlinear Equations

For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions \cn(x,m) and \dn(x,m) with modulus $m$, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schr\"odinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schr\"odinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schr\"odinger equation, $\lambda \phi^4$, the discrete MKdV as well as for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of \dn^2(x,m), it also admits solutions in terms of \dn^2(x,m) \pm \sqrt{m} \cn(x,m) \dn(x,m), even though \cn(x,m) \dn(x,m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations.Comment: 40 pages, no figure

Two-mode Nonlinear Coherent States

Two-mode nonlinear coherent states are introduced in this paper. The pair coherent states and the two-mode Perelomov coherent states are special cases of the two-mode nonlinear coherent states. The exponential form of the two-mode nonlinear coherent states is given. The photon-added or photon-subtracted two-mode nonlinear coherent states are found to be two-mode nonlinear coherent states with different nonlinear functions. The parity coherent states are introduced as examples of two-mode nonlinear coherent states, and they are superpositions of two corresponding coherent states. We also discuss how to generate the parity coherent states in the Kerr medium.Comment: 11 pages, no figures, accepted for publication in Optics Communication

Nonlinear waves of nuclear density

Nonlinear excitations of nuclear density are considered in the framework of semiclassical nonlinear nuclear hydrodynamics. Possible types of stationary nonlinear waves in nuclear media are analysed using Nonlinear Schroedinger equation of fifth order and classified using a simple mechanical picture. It is shown that a rich spectrum of nonlinear oscillations in one-dimensional nuclear medium exist.Comment: 18 pages, 5 figure