Painleve analysis and traveling wave solutions of the sixth order differential equation with non-local nonlinearity

In this paper, we study a nonlinear partial differential equation for describing high dispersion optical soliton with non-local nonlinearity. Taking into account the traveling wave reduction, we get system of ordinary differential equations (ODEs) for real and imaginary parts of the original equation. To determine the integrability of equation we apply the Painleve test for analysis of obtained ODE system. We illustrate that the system of equations does not have the Painleve property since there is only one integer Fuchs index. However using the Painleve data we find the compatibility conditions for the ODE system. Under these conditions, the traveling wave solution of nonlinear differential equations are constructed and illustrated.

Automated summary

This paper studies a nonlinear partial differential equation describing high dispersion optical soliton with non-local nonlinearity. By considering the traveling wave reduction, a system of ODEs for the real and imaginary parts of the original equation is derived. The Painleve test is used to analyze the integrability of the equation, and although the system does not have the Painleve property, compatibility conditions are found for constructing traveling wave solutions of the nonlinear differential equations using the Painleve data.