International consensus has been reached on the principles regarding evaluation of the food safety of genetically modi®ed plants. The concept of substantial equivalence has been developed as part of a safety evaluation framework, based on the idea that existing foods can serve as a basis for comparing the properties of genetically modi®ed foods with the appropriate counterpart. Application of t...

We discuss the recent paper by Inan and Ugurlu [Inan I.E., Ugurlu Y., Exp-function method for the exact solutions of fifth order KdV equation and modified Burgers equation, Appl. Math. Comp. 217 (2010) 1294 – 1299]. We demonstrate that all exact solutions of fifth order KdV equation and modified Burgers equation by Inan and Ugurlu are trivial solutions that are reduced to constants. Moreover, w...

Long's equation describes stationary flows to all orders of nonlinearity and dispersion. Dissipation is neglected. In this paper, Long's equation is used to attempt to model the propagation of a solibore -a train of internal waves in shallow water at the deepening phase of the internal tide. 1. The Solibore Phenomenon The internal tide in shallow water often has a sawtooth shape rather than a s...

Abstract: In this paper, we studied the numerical solution of a time-fractional Korteweg–de Vries (KdV) equation with new generalized fractional derivative proposed recently. The fractional derivative employed in this paper was defined in Caputo sense and contained a scale function and a weight function. A finite difference/collocation scheme based on Jacobi–Gauss–Lobatto (JGL) nodes was applie...

The dynamics of the highly nonlinear fifth order KdV-type equation is discussed in the framework of the Lagrangian and Hamiltonian formalisms. The symmetries of the Lagrangian produce three commuting conserved quantities that are found to be recursively related to one-another for a certain specific value of the power of nonlinearity. The above cited recursion relations are obeyed with a second ...

Circuit Simulation Lu s Miguel Silveira Jacob White Steven Leeb Research Laboratory of Electronics Dept. of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge, MA 02139 Abstract In this paper, a modi ed envelope-following method for simulation of clocked analog circuits is described. The modi cation makes the envelope-following algorithm more e cient, as...

In this paper a modi"ed version of the standard least-squares algorithm is presented. The aim is to use the proposed modi"ed LS algorithm in linear time-varying systems. The proposed modi"cation involves the addition of extra terms to both the parameter estimates' and the covariance's update laws. We establish a series of properties on the identi"cation error, the parameter estimates and the co...

A quantum theory is developed for a difference-difference system which can serve as a toy-model of the quantum Korteveg-de-Vries equation. Introduction This Letter presents an example of a completely integrable ‘discrete-space-time quantum model’ whose Heisenberg equations of motion have the form φ (τ, n) φ (τ, n− 1) + λ φ (τ, n− 1) φ (τ − 1, n− 1) = λ φ (τ, n) φ (τ − 1, n) + φ (τ − 1, n) φ (τ ...

Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this paper. It is shown that the Bäcklund transform is...

If the initial condition for the Korteweg-deVries (KdV) equation is a weakly nonlinear wavepacket, then its evolution is described by the Nonlinear Schrödinger (NLS) equation. This KdV/NLS connection has been known for many years, but its various aspects and implications have been discussed only in asides. In this note, we attempt a more focused and comprehensive discussion including such as is...