given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

This paper studies dispersive bright and dark optical solitons, modeled by the Schrödinger–Hirota equation, numerically aid of Adomian decomposition. The surface plots algorithm yielded an impressively small measure. effects soliton radiation are ignored.

It is shown that the celebrated Menelaus relation, Hirota–Miwa bilinear equation for KP hierarchy and Fay's trisecant formula similar to WDVV are associativity conditions structure constants of certain three-dimensional quasi-algebra.

As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of ...

A new iterative technique is employed to solve a system of nonlinear fractional partial differential equations. This new approach requires neither Lagrange multiplier like variational iteration method VIM nor polynomials like Adomian’s decomposition method ADM so that can be more easily and effectively established for solving nonlinear fractional differential equations, and will overcome the li...

Article history: Received 28 January 2011 Received in revised form 28 March 2011 Accepted 22 April 2011 Available online 29 April 2011 Communicated by R. Wu

In this paper, a generalized long-wave short-wave resonance interaction system, which describes the nonlinear between and in fluid dynamics, plasma physics optics, is considered. Using Hirota bilinear method, general N-bright N-dark soliton solutions are deduced their Gram determinant forms obtained. A special feature of fundamental bright solution that, general, it behaves like Korteweg-deVrie...