中文摘要：

Fokas system is the simplest（2+1）-dimensional extension of the nonlinear Schrodinger equation（Eq.（2）,Inverse Problems 10（1994） L19-L22）.By using the bilinear transformation method,general rational solutions for the Fokas system are given explicitly in terms of two order-N determinants Tn（n = 0,1） whose elements mi,jn（n = 0,1;1≤i,j≤N）are involved with order-niand order-njderivatives.When N = 1,three kinds of rational solution,i.e.,fundamental lump and fundamental rogue wave（RW） with n1= 1,and higher-order rational solution with n1> 2,are illustrated by explicit formulas from Tn（n = 0,1） and pictures.The fundamental RW is a line RW possessing a line profile on（x,y）-plane,which arises from a constant background with at t << 0 and then disappears into the constant background gradually at t >> 0.The fundamental lump is a traveling wave,which can preserve its profile during the propagation on（x,y）-plane.When N ≥2 and n1=n2=...=nn= 1,several specific multi-rational solutions are given graphically.

英文摘要：

Fokas system is the simplest（2+1）-dimensional extension of the nonlinear Schrodinger equation（Eq.（2）,Inverse Problems 10（1994） L19-L22）.By using the bilinear transformation method,general rational solutions for the Fokas system are given explicitly in terms of two order-N determinants Tn（n = 0,1） whose elements mi,jn（n = 0,1;1≤i,j≤N）are involved with order-niand order-njderivatives.When N = 1,three kinds of rational solution,i.e.,fundamental lump and fundamental rogue wave（RW） with n1= 1,and higher-order rational solution with n1> 2,are illustrated by explicit formulas from Tn（n = 0,1） and pictures.The fundamental RW is a line RW possessing a line profile on（x,y）-plane,which arises from a constant background with at t << 0 and then disappears into the constant background gradually at t >> 0.The fundamental lump is a traveling wave,which can preserve its profile during the propagation on（x,y）-plane.When N ≥2 and n1=n2=...=nn= 1,several specific multi-rational solutions are given graphically.