2019
Том 71
№ 11

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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.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 44 (1992), no. 9, pp 1156–1166.

Citation Example: Syroyid I. -P. P. 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 // Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1264-1275.

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