TY - JOUR
T1 - A systematic method for solving differential-difference equations
AU - Zhang, Yufeng
AU - Hon, Y. C.
AU - Mei, Jianqin
PY - 2010/10
Y1 - 2010/10
N2 - A systematic method for searching travelling-wave solutions to differential-difference equations (DDEs) is proposed in the paper. First of all, we introduce Bäcklund transformations for the standard Riccati equation which generate new exact solutions by using its simple and known solutions. Then we introduce a kind of formal polynomial solutions to DDEs and further determine the explicit forms by applying the balance principle. Finally, we work out exact solutions of the DDEs via substituting the form solutions and solving over-determined algebraic equations with the help of Maple. As illustrative examples, we obtain the travelling-wave solutions of the (2 + 1)-dimensional Toda lattice equation, the discrete modified KdV (mKdV) equation, respectively. © 2009 Elsevier B.V. All rights reserved.
AB - A systematic method for searching travelling-wave solutions to differential-difference equations (DDEs) is proposed in the paper. First of all, we introduce Bäcklund transformations for the standard Riccati equation which generate new exact solutions by using its simple and known solutions. Then we introduce a kind of formal polynomial solutions to DDEs and further determine the explicit forms by applying the balance principle. Finally, we work out exact solutions of the DDEs via substituting the form solutions and solving over-determined algebraic equations with the help of Maple. As illustrative examples, we obtain the travelling-wave solutions of the (2 + 1)-dimensional Toda lattice equation, the discrete modified KdV (mKdV) equation, respectively. © 2009 Elsevier B.V. All rights reserved.
KW - Differential-difference equation
KW - Exact solution
KW - Lattice equation
UR - http://www.scopus.com/inward/record.url?scp=77950859027&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-77950859027&origin=recordpage
U2 - 10.1016/j.cnsns.2009.10.019
DO - 10.1016/j.cnsns.2009.10.019
M3 - RGC 21 - Publication in refereed journal
SN - 1007-5704
VL - 15
SP - 2791
EP - 2797
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
IS - 10
ER -