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

• Date: 1992
• Main Authors: Siroid , I.-P. P., Сироїд , І.-П. П.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 1992
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8179
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...