arXiv subjects

S. Vijayalakshmi

Publications and source records attributed to S. Vijayalakshmi.

5 recordsLinked to original sources

arXiv2004

Localized Coherent Structures of Ishimori Equation I through Hirota's Bilinearization method:Time dependent/Stationary boundaries

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.

nlin.SI↗

arXiv1999

Explode-decay dromions in the non-isospectral Davey-Stewartson I (DSI) equation

In this letter, we report the existence of a novel type of explode-decay dromions, which are exponentially localized coherent structures whose amplitude varies with time, through Hirota method for a nonisospectral Davey-Stewartson equation I discussed recently by Jiang. Using suitable transformations, we also point out such solutions also exist for the isospectral Davey-Stewartson I equation itself for a careful choice of the potentials.

math.AP↗

arXiv1998

Motion of Curves and Surfaces and Nonlinear Evolution Equations in (2+1) Dimensions

It is shown that a class of important integrable nonlinear evolution equations in (2+1) dimensions can be associated with the motion of space curves endowed with an extra spatial variable or equivalently, moving surfaces. Geometrical invariants then define topological conserved quantities. Underlying evolution equations are shown to be associated with a triad of linear equations. Our examples include Ishimori equation and Myrzakulov equations which are shown to be geometrically equivalent to Davey-Stewartson and Zakharov -Strachan (2+1) dimensional nonlinear Schrödinger equations respectively.

solv-int↗

arXiv1998

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↗

arXiv1997

A (2+1) dimensional integrable spin model: Geometrical and gauge equivalent counterpart, solitons and localized coherent structures

A non-isospectral (2+1) dimensional integrable spin equation is investigated. It is shown that its geometrical and gauge equivalent counterparts is the (2+1) dimensional nonlinear Schrödinger equation introduced by Zakharov and studied recently by Strachan. Using a Hirota bilinearised form, line and curved soliton solutions are obtained. Using certain freedom (arbitrariness) in the solutions of the bilinearised equation, exponentially localized dromion-like solutions for the potential is found. Also, breaking soliton solutions (for the spin variables) of the shock wave type and algebraically localized nature are constructed.

solv-int↗