Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic pot...Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.展开更多
We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regu...We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos.11375030 and 61304133
文摘Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.
基金supported by the Army Research Office under DAAD19-02-1-0394,US-ARO grant 49308MA and US-AFSOR grant FA9550-06-1-0241
文摘We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.
