In this paper, we suggest and analyze a new four-step iterative method for solving nonlinear equations involving only first derivative of the function using a new decomposition technique which is due to Noor [11] and Noor and Noor [16]. We show that this new iterative method has fifth-order of convergence. Several numerical examples are given to illustrate the efficiency and performance of the ...

Some of the well-known convergence acceleration algorithms, when viewed as two-variable difference equations, are equivalent to discrete soliton equations. It is shown that the η−algorithm is nothing but the discrete KdV equation. In addition, one generalized version of the ρ−algorithm is considered to be integrable discretization of the cylindrical KdV equation. ‡ E-mail: [email protected]...

A quantum lattice gas representation is determined for both the non-linear Schrödinger (NLS) and Korteweg–de Vries (KdV) equations. There is excellent agreement with the solutions from these representations to the exact soliton–soliton collisions of the integrable NLS and KdV equations. These algorithms could, in principle, be simulated on a hybrid quantum-classical computer.  2003 Elsevier Sc...

We prove that one system of coupled KdV equations, recently claimed by Hirota, Hu and Tang [J. Math. Anal. Appl. 288:326–348 (2003)] to pass the Painlevé test for integrability, actually fails the test at the highest resonance of the generic branch. Introduction In Section 6 of their recent work [1], Hirota, Hu and Tang reported that the system of coupled KdV equations ∂ui ∂t + 6a ( N

In this study, a new modification of the newly developed semi-analytical method, optimal auxiliary function method (OAFM) is used for fractional-order KdVs equations. This called fractional (FOAFM). The time derivatives are treated with Caputo sense. A rapidly convergent series solution obtained from FOAFM and validated by comparing other results. analysis proves that our simplified applicable,...

Quantum monodromy matrices coming from a theory of two coupled (m)KdV equations are modified in order to satisfy the usual Yang-Baxter relation. As a consequence, a general connection between braided and unbraided (usual) Yang-Baxter algebras is derived and also analysed.

In this article we apply the modified extended tanh-function method to find the exact traveling wave solutions of the generalized KdV-mKdV equation with any order nonlinear terms. This method presents a wider applicability for handling many other nonlinear evolution equations in mathematical physics.

A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schrödinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturbation theory, based on linear boosts and Gallilean transformations, is often employed to establish connections to and between such universal equati...