A new multicomponent CKP hierarchy and solutions

Abstract

Based on the eigenfunction symmetry constraints, we first propose a new multicomponent C-type subhierarchy for Kadomtsev-Petviashvili (mcCKP) hierarchy and its Lax representation, which provides an effective way to find two types of new CKP equation with self-consistent sources along with their related Lax representations. Also it admits reductions to k-constrained CKP hierarchy and to a (1+1)-dimensional soliton hierarchy with self-consistent sources, which gives rise to two types of new Kaup–Kuperschmidt (KK) equation with self-consistent sources and two types of new bidirectional Kaup–Kuperschmidt equation with self-consistent sources. By using the solutions of the CKP and KK equations and their corresponding eigenfunctions, N-soliton solutions for the first type of CKP self-consistent source (CKPSCS) and of KKSCS are constructed by means of method of variation in constant, respectively.