2019
Том 71
№ 11

All Issues

Syroyid I. -P. P.

Articles: 1
Article (Ukrainian)

Matrix solutions of the equation $\mathfrak{B}U_t = - U_{xx} + 2U^3 + \mathfrak{B}[U_x ,U] + 4cU:$ extension of the method of the inverse scattering problem

Syroyid I. -P. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1264-1275

Complex solution matrices of the nonlinear Schrödinger equation $\mathfrak{B}U_t = - U_{xx} + 2U^3 + \mathfrak{B}[U_x ,U] + 4cU:$ are found and the method of the inverse scattering problem is subjected to a natural extension. That is, for the nonself-conjugate $L-A$ Lax doublet that arises for this equation, the presence of chains of adjoint vectors for the operator $L$ is taken into account by means the corresponding normed chains. A uniqueness theorem for the Cauchy problem for the above Schrödinger equation is obtained. Here $$\mathfrak{B} = \left( {\begin{array}{*{20}c} 0 & 1 \\ { - 1} & 0 \\ \end{array} } \right),[M,N] = MN - NM$$ and $c$ is a parameter.