The Integrability of a New Fractional Soliton Hierarchy and Its Application
Xiaoming Zhu, Jian‐bing Zhang
Abstract
Two fractional soliton equations are presented generated from the same spectral problem involved in a fractional potential by the zero-curvature representations. They are a kind of special reductions of the famous AKNS system. The two equations are integrable for they both possess explicit soliton solutions constructed by the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>N</a:mi> <a:mo>−</a:mo> </a:math> fold Darboux transformation. As an application of the obtained solutions, new soliton solutions of the classic <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mfenced open="(" close=")"> <c:mrow> <c:mn>2</c:mn> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:mrow> </c:mfenced> </c:math> -dimensional Kadometsev-Petviashvili (KP) equation are soughed out by a cubic polynomial relation. Dynamic properties are analyzed in detail.