Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2004-08-19
Nonlinear Sciences
Exactly Solvable and Integrable Systems
17 Pages and 3 Figures
Scientific paper
Ishimori equation is a $(2+1)$ dimensional generalization of the $(1+1)$ dimensional integrable classical continuous Heisenberg ferromagnetic spin equation. The richness of the coherent structures admitted by Ishimori equation I such as dromion, lump and rationally- exponentially localized solutions, have been demonstrated in the literature through $\bar \partial$ technique and binary Darboux transformation method. To our knowledge Hirota's method had been adopted to construct only the vortex solutions of Ishimori equation II. For the first time, the various types of localized coherent structures mentioned above have been constructed in this paper for the Ishimori equation I using the Hirota's direct method. In particular we have brought out the significance of boundaries and arbitrary functions in generating all these types of localized structures and proved that the absence of such boundaries leads only to line soliton solutions.
Lakshmanan Meenakshi
Vijayalakshmi S.
No associations
LandOfFree
Localized Coherent Structures of Ishimori Equation I through Hirota's Bilinearization method:Time dependent/Stationary boundaries does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Localized Coherent Structures of Ishimori Equation I through Hirota's Bilinearization method:Time dependent/Stationary boundaries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Localized Coherent Structures of Ishimori Equation I through Hirota's Bilinearization method:Time dependent/Stationary boundaries will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-84245