具有加权Sobolev空间初值的耦合Kundu-非线性Schrödinger方程的孤子分解

通过发展■-非线性速降方法,本文研究Kundu-非线性Schrodinger(Kundu-nonlinear Schrodinger,KN-NLS)方程在t趋向无穷时解的长时间渐近行为.在初值u0(x),v0(x)∈H^(1,1)(R)=H^(1)(R)∩L^(2,1)(R)时,本文证明耦合KN-NLS方程的解可以分解为有限个孤子的和与色散分量.更进一步地,在给定的锥C(x1,x2,v1,v2)={(x,t)∈R^(2):x=x0+vt,x0∈[x1,x2],v∈[v1,v2]}中,本文证明可用锥中有限孤子来逼近N孤子解.本文结果也表明,当初值属于加权Sobolev空间时,耦合KN-NLS方程的孤子分解猜想是成立的.

Inverse Scattering Transform and Soliton Solutions for the Hirota Equation with N Distinct Arbitrary Order Poles

We employ the Riemann-Hilbert(RH)method to study the Hirota equation with arbitrary order zero poles under zero boundary conditions.Through the spectral analysis,the asymptoticity,symmetry,and analysis of the Jost functions are obtained,which play a key role in constructing the RH problem.Then we successfully established the exact solution of the equation without reflection potential by solving the RH problem.Choosing some appropriate parameters of the resulting solutions,we further derive the soliton solutions with different order poles,including four cases of a fourthorder pole,two second-order poles,a third-order pole and a first-order pole,and four first-order points.Finally,the dynamical behavior of these solutions are analyzed via graphic analysis.