Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1998-03-13
J. Math. Phys. vol.39 (1998) 2122-2140
Nonlinear Sciences
Exactly Solvable and Integrable Systems
32 pages, no figures, accepted for publication in J. Math. Phys
Scientific paper
10.1063/1.532279
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 Schr\"odinger 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.
Lakshmanan Meenakshi
Myrzakulov Ratbay
Syzdykova R. N.
Vijayalakshmi S.
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