the purpose of this paper is to study the convergence and the almost sure t-stability of the modied sp-type random iterative algorithm in a separable banach spaces. the bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure t-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. our resu...

The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all L 2-based Sobolev spaces H s where local well-posedness is presently known, apart from the H 1 4 (R) endpoint for mKdV. The result for KdV relies on a new method for co...

based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the korteweg-de vries (kdv) equation are first constructed by the known darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude de...

In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using a new approach by combining cubic B-spline functions. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms L2, L∞ are computed. Three invariants of motion are...

In this paper we find a explicit moving frame along curves of Lagrangian planes invariant under the action of the symplectic group. We use the moving frame to find a family of independent and generating differential invariants. We then construct geometric Hamiltonian structures in the space of differential invariants and prove that, if we restrict them to a certain Poisson submanifold, they bec...

The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. It is shown that for H initial data, s > −1/2, and for any s1 < min(3s+1, s+ 1), the difference of the nonlinear and linear evolutions is in H1 for all times, with at most polynomially growing H1 norm. The result also extends to KdV with a smooth, mean zero, time-dependent potential in the case s ≥ 0. Our resu...

On the exact solutions of integrable models, there is a new classification way recently based on the property of associated spectral parameters [1]. Negatons, related to the negative spectral parameter, are usually expressed by hyperbolic functions, and positons are expressed by means of trigonometric functions related to the positive spectral parameters. The so-called complexiton, which is exp...

1 A modi ed lattice structure with pleasant scaling properties Jean Laroche Abstract| This communication presents a modi ed lattice structure for IIR lters, which exhibits pleasant scaling properties at no additional computational or memory cost when the re ection coe cients are close to 1. With this structure, the gain at the resonance of a second-order purely-recursive section is nearly indep...

We propose integrable discretizations of derivative nonlinear Schrödinger (DNLS) equations such as the Kaup–Newell equation, the Chen–Lee–Liu equation and the Gerdjikov–Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reduc...

We investigate the integrability of Nonlinear Partial Differential Equations (NPDEs). The concepts are developed by firstly discussing the integrability of the KdV equation. We proceed by generalizing the ideas introduced for the KdV equation to other NPDEs. The method is based upon a linearization principle which can be applied on nonlinearities which have a polynomial form. We illustrate the ...