36 citations · 60 across the 12 of their papers we have counts for
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Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions
Alexander Sakhnovich
Auxiliary systems for matrix nonisospectral equations, including coupled NLS with external potential and KdV with variable coefficients, were introduced. Explicit solutions of noni…
On a new integrable nonlinear Schroedinger equation with a simple external potential and its explicit solutions
Alexander Sakhnovich
A nonlinear Schrödinger equation with external potential is considered and its explicit solutions are constructed.
Harmonic maps, Backlund-Darboux transformations and "line soliton" analogs
Alexander Sakhnovich
Harmonic maps from $\BR^2$ or one-connected domain $Ø\subset \BR^2$ into $GL(m, \BC)$ and are treated. The GBDT version of the Bäcklund-Darboux transformation is applied to…
Second harmonic generation: Goursat problem on the semi-strip and explicit solutions
Alexander Sakhnovich
A rigorous and complete solution of the initial-boundary-value (Goursat) problem for second harmonic generation (and its matrix analog) on the semi-strip is given in terms of the W…
Discrete canonical system and non-Abelian Toda lattice: Backlund-Darboux transformation and Weyl functions
Alexander Sakhnovich
A version of the iterated Bäcklund-Darboux transformation, where Darboux matrix takes a form of the transfer matrix function from the system theory, is constructed for the discrete…