Abstract
The Lie point symmetries are reported by performing the Lie symmetry analysis to the Ablowitz-Kaup-Newell-Suger (AKNS) equation with time-dependent coefficients. In addition, the optimal system of one-dimensional subalgebras is constructed. Based on this optimal system, several categories of similarity reduction and some new invariant solutions for the equation are obtained, which include power series solutions and travelling and non-traveling wave solutions.
Highlights
The term nonlinear partial differential equation (NLPDE) is broadly utilized as a model in order to represent actual phenomena that occur many science areas, in plasma physics, optical fields, and fluid mechanics
We construct the optimal system of one-dimensional subalgebras of Lie algebra spanned by V1 − V3
Five types of similarity reduction are presented by using the optimal system
Summary
The term nonlinear partial differential equation (NLPDE) is broadly utilized as a model in order to represent actual phenomena that occur many science areas, in plasma physics, optical fields, and fluid mechanics. As well as we know, Lie symmetry analysis is a powerful and prolific method for constructing exact solutions for NLPDEs with constant variable [18,19,20]. The Lie symmetry analysis is extended to find exact solutions of fractional and variable coefficient NLPDEs, such as Time-Fractional. Zhang et al [27] studied the multi-soliton solutions of the following Ablowitz- KaupNewell-Suger (AKNS) equation qt = α3 (t)(qxxx − 6qrqx ) + α2 (t)(−qxx + 2q2 r) + α1 (t)qx − α0 (t)q, rt = α3 (t)(rxxx − 6qrrx ) + α2 (t)(rxx − 2r2 q) + α1 (t)rx + α0 (t)r,. The AKNS equation with time-dependent coefficients has not been studied via Lie symmetry analysis. The aim of the present paper is to construct optimal system and invariant solutions to (1) based on Lie point symmetries.
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