Matrix solutions of the equations $\mathfrak{B}U_t= -U_{xx} + 2U^3+\mathfrak{B} [U_x,U]+4cU$: development of the method of the inverse problem of dissipation
Complex solution matrices of the nonlinear Schrödinger equation $\mathfrak{B}Ut = -U_{xx}+2U^3+\mathfrak{B}[U_x, U]+4cU$ are found and the method of the inverse scattering problem is subjected to a natural extension. That is, for the nonself-conjugate $\tilde L — А$ Lax doublet that arises for this...
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| Datum: | 1992 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8179 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Complex solution matrices of the nonlinear Schrödinger equation $\mathfrak{B}Ut = -U_{xx}+2U^3+\mathfrak{B}[U_x, U]+4cU$ are found and the method of the inverse scattering problem is subjected to a natural extension. That is, for the nonself-conjugate $\tilde L — А$ Lax doublet that arises for this equation, the presence of chains of adjoint vectors for the operator $\tilde L$  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 $\mathfrak{B}=\begin{pmatrix} 0 & 1 \\ -1 & 0\end{pmatrix}, [M, N] = MN — NM$, and $c$ is a parameter. |
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