$L^{2}$-Sobolev space bijectivity and existence of global solutions for
the matrix nonlinear Schr\"{o}dinger equations
$L^{2}$-Sobolev space bijectivity and existence of global solutions for
the matrix nonlinear Schr\"{o}dinger equations
We consider the Cauchy problem to the general defocusing and focusing $p\times q$ matrix nonlinear Schr\"{o}dinger (NLS) equations with initial data allowing arbitrary-order poles and spectral singularities. By establishing the $L^{2}$-Sobolev space bijectivity of the direct and inverse scattering transforms associated with a $(p+q)\times(p+q)$ matrix spectral problem, we prove that …