Auto-Bäcklund Transformation and Extended Tanh-Function Methods to Solve the Time-Dependent Coefficients Calogero-Degasperis Equation

Abstract

In this paper, the Auto-Bäcklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Calogero-Degasperis (VCCD) equation. New soliton and periodic solutions of many types are obtained. Furthermore, the soliton propagation is discussed under the effect of the variable coefficients.

Lie symmetry analysis of a variable coefficient Calogero–Degasperis equation

“…A variable coefficient equation that generalizes equation (1) has the form which has been studied from different points of view. See, for example, in [12][13][14][15]. We assume that ( ) f t , ( ) g t and ( ) h t are nonzero smooth functions.…”