TY - JOUR
T1 - Negaton and positon solutions of the soliton equation with self-consistent sources
AU - Zeng, Yunbo
AU - Shao, Yijun
AU - Xue, Weimin
PY - 2003/5/9
Y1 - 2003/5/9
N2 - The Korteweg-de Vries (KdV) equation with self-consistent sources (KdVES) is used as a model to illustrate this method. We present a generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for N-times repeated GBDT. This GBDT provides non-auto-Bäcklund transformation between two KdV equations with different degrees of sources and enables us to construct more general solutions with N arbitrary t-dependent functions. By taking the special t-function, we obtain multisoliton, multipositon, multinegaton, multisoliton-positon, multinegaton-positon and multisoliton-negaton solutions of the KdVES.
AB - The Korteweg-de Vries (KdV) equation with self-consistent sources (KdVES) is used as a model to illustrate this method. We present a generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for N-times repeated GBDT. This GBDT provides non-auto-Bäcklund transformation between two KdV equations with different degrees of sources and enables us to construct more general solutions with N arbitrary t-dependent functions. By taking the special t-function, we obtain multisoliton, multipositon, multinegaton, multisoliton-positon, multinegaton-positon and multisoliton-negaton solutions of the KdVES.
UR - http://www.scopus.com/inward/record.url?scp=0038736753&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/36/18/308
DO - 10.1088/0305-4470/36/18/308
M3 - Journal article
AN - SCOPUS:0038736753
SN - 0305-4470
VL - 36
SP - 5035
EP - 5043
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 18
ER -