Singularity formation and blowup of complex-valued solutions of the modified KdV equation

Singularity formation and blowup of complex-valued solutions of the modified KdV equation

The dynamics of the poles of the two–soliton solutions of the modified Korteweg–de Vries equation ut + 6u ux + uxxx = 0 are determined. A consequence of this study is the existence of classes of smooth, complex–valued solutions of this equation, defined for−∞ < x < ∞, exponentially decreasing to zero as |x| → ∞, that blow up in finite time.

formation and evolution of regional organizations: the case study of the economic cooperation organization (eco)

abstract because of the many geopolitical, geo economical and geo strategically potentials and communicational capabilities of eco region, members can expand the convergence and the integration in base of this organization that have important impact on members development and expanding peace in international and regional level. based on quality analyzing of library findings and experts interv...

Application of the Kudryashov method and the functional variable method for the complex KdV equation

In this present work, the Kudryashov method and the functional variable method are used to construct exact solutions of the complex KdV equation. The Kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.

Exp-function method for the exact solutions of fifth order KdV equation and modified Burgers equation

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...

NONANALYTIC SOLUTIONS OF THE KdV EQUATION