Painlevé Analysis and Infinite Lie Symmetries of the Complex Modified Korteweg-De Vries-II Equation

Authors

Abulgassim Ali MUHAMMAD
Mehmet CAN

DOI

-

Abstract

The Painleve analysis developed by Weiss et al. [9] for nonlinear partial differential equations is applied to the CMKdV-II equation. It has been shown that this equation passes the Painleve test. By specializing the arbitrary functions that appear in the phi series expansions found in the test, one obtains a system of partial differential equations for the formally arbitrary data. For specific systems, and conjectured in general, these equations are integrable. The form of the resulting reduction enables the identification of integrable reductions of the original systems. Assuming u_i = \upsilon_i = 0, i >= 2 we obtain conditions to have truncated series solutions. Then the data obtained by this truncation technique are used to develop some analytical solutions and infinite dimensional Lie symmetries of the equation.

First Page

303

Last Page

309

Recommended Citation

MUHAMMAD, Abulgassim Ali and CAN, Mehmet (1997) "Painlevé Analysis and Infinite Lie Symmetries of the Complex Modified Korteweg-De Vries-II Equation," Turkish Journal of Mathematics: Vol. 21: No. 3, Article 6. Available at: https://journals.tubitak.gov.tr/math/vol21/iss3/6