On the Soliton Geometry in Multidimensions
Some aspects of the multidimensional soliton geometry are considered.
math.DG↗
arXiv subjects
R. N. Syzdykova
Publications and source records attributed to R. N. Syzdykova.
Soliton equations in 2+1 dimensions: reductions, bilinearizations and simplest solutions
Soliton equations in 2+1 and their 1+1 = 2+0 reductions are considered.
solv-int↗
On some soliton equations in 2+1 dimensions and their 1+1 and/or 2+0 dimensional integrable reductions
Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.
solv-int↗
On the simplest (2+1) dimensional integrable spin systems and their equivalent nonlinear Schrödinger equations
Using a moving space curve formalism, geometrical as well as gauge equivalence between a (2+1) dimensional spin equation (M-I equation) and the (2+1) dimensional nonlinear Schrödinger equation (NLSE) originally discovered by Calogero, discussed then by Zakharov and recently rederived by Strachan, have been estabilished. A compatible set of three linear equations are obtained and integrals of motion are discussed. Through stereographic projection, the M-I equation has been bilinearized and different types of solutions such as line and curved solitons, breaking solitons, induced dromions, and domain wall type solutions are presented. Breaking soliton solutions of (2+1) dimensional NLSE have also been reported. Generalizations of the above spin equation are discussed.
solv-int↗