Abstract
We examine the integrability in terms of Painlevè analysis for several models of higher order nonlinear solitary wave equations which were recently derived by Christou. Our results point out that these equations do not possess Painlevè property and fail the Painlevè test for some special values of the coefficients; and that indicates a non-integrability criteria of the equations by means of the Painlevè integrability.
Highlights
A variety of new nonlinear partial differential equations were recently introduced in the work of [1] from applying a different type of techniques; The author managed to exploit fundamental physics laws, Taylor series expansion and Hirota’s bilinear operator to derive some higher order solitary wave equations
We shall inspect Painlevè integrability for the equations (1), (2) and (3); and the integrability means here is that the differential equation does have Painlevè property
The equation does not pass the Painlevè test which indicates that the equation does not have a single valued around movable singularity, but it may have a movable algebraic or logarithmic branch point
Summary
A variety of new nonlinear partial differential equations were recently introduced in the work of [1] from applying a different type of techniques; The author managed to exploit fundamental physics laws, Taylor series expansion and Hirota’s bilinear operator to derive some higher order solitary wave equations. The first model, the sixth order solitary wave equation using Ohm’s law is given by (1) where is a function of and , the subscripts denote to partial derivatives with respect to the independent variables, and. The rest of the paper is organized as follows, in section two the Painlevè analysis for the sixth order solitary wave equations using Ohm’s law is considered, section three is dedicated to apply the Painlevè test for the nonlinear sixth order equation using Hirota’s bilinear operator.
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