The initial–boundary value problem for the Schrödinger–Korteweg–de Vries system is considered on the left and right half-lines for a wide class of initial–boundary data, including the energy regularity \(H^1({\mathbb {R}}^{\pm })\times H^1({\mathbb {R}}^{\pm })\) for initial data. Assuming homogeneous boundary conditions, for the problem on the positive half-line, it is shown for positive coupling interactions that local solutions can be extended globally in time for initial data in the energy space. Furthermore, for negative coupling interactions, for a certain class of regular initial data, the following result was proved: if the respective solution does not exhibit finite-time blow-up in \(H^1({\mathbb {R}}^-)\times H^1({\mathbb {R}}^-)\), then the norm of the weighted space \(L^2\big ({\mathbb {R}}^-,\, |x|\mathrm{d}x\big )\times L^2\big ({\mathbb {R}}^-,\, |x|\mathrm{d}x\big )\) blows up at infinity time with super-linear rate; this is obtained by using a satisfactory algebraic manipulation of a new global virial-type identity associated with the system, which does not work in the context of whole real line.

对于一大类初始边界数据，包括能量规则性\（H ^ 1（{\ mathbb {R }} ^ {\ pm}）\初始数据的时间H ^ 1（{\ mathbb {R}} ^ {\ pm}）\）。假设边界条件是均匀的，那么对于正半线上的问题，对于正耦合相互作用，它表明局部解可以在时间上全局扩展以获取能量空间中的初始数据。此外，对于负耦合相互作用，对于特定类别的常规初始数据，证明了以下结果：如果各个解在\（H ^ 1（{\ mathbb {R}} ^ -）\ times H ^ 1（{\ mathbb {R}} ^-）\），然后是加权空间的范数\（L ^ 2 \ big（{\ mathbb {R}} ^-，\，| x | \ mathrm {d} x \ big）\ times L ^ 2 \ big（{\ mathbb {R}} ^-， \，| x | \ mathrm {d} x \ big）\）在无穷大时以超线性速率爆炸；这是通过使用与系统关联的新的全局病毒式身份的令人满意的代数操作获得的，该身份在整个实线环境中均不起作用。