This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the ...This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the subsonic limit. After obtaining some a priori estimates,we prove under certain natural conditions that the solutions to the Cauchy problem of the vector nonlinear Schrdinger equations in two and three spatial dimensions blow up in a finite time. Assuming that a solution to the aforementioned vector nonlinear Schrdinger equations is radially symmetric with respect to spatial variables x,we show that if the initial energy is non-positive,then the solution blows up in three dimensions in a finite time.展开更多
We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed...We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs.The construction is based on the so-called dressing the boundary,which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process.Under the Robin BCs,examples,including boundary-bound solitons,are explicitly derived;under the mixed Neumann/Dirichlet BCs,the boundary can act as a polarizer that tunes different components of the vector solitons.Connection of our construction to the inverse scattering transform is also provided.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11171241, 10801102, 11071177)
文摘This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the subsonic limit. After obtaining some a priori estimates,we prove under certain natural conditions that the solutions to the Cauchy problem of the vector nonlinear Schrdinger equations in two and three spatial dimensions blow up in a finite time. Assuming that a solution to the aforementioned vector nonlinear Schrdinger equations is radially symmetric with respect to spatial variables x,we show that if the initial energy is non-positive,then the solution blows up in three dimensions in a finite time.
文摘We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs.The construction is based on the so-called dressing the boundary,which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process.Under the Robin BCs,examples,including boundary-bound solitons,are explicitly derived;under the mixed Neumann/Dirichlet BCs,the boundary can act as a polarizer that tunes different components of the vector solitons.Connection of our construction to the inverse scattering transform is also provided.
