Chin. Phys. B, 2014, Vol. 23(1): 010307    DOI: 10.1088/1674-1056/23/1/010307
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# Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation

B. Srividyaa b, L. Kavithaa c, R. Ravichandrana, D. Gopic d
a Department of Physics, Periyar University, Salem 636 011, India;
b Department of Physics, K.S.R. College of Engineering, Tiruchengode 637 215, India;
c Centre for Nanoscience and Nanotechnology, Periyar University, Salem 636 011, India;
d Department of Chemistry, Periyar University, Salem 636 011, India
Abstract  We show by an extensive method of quasi-discrete multiple-scale approximation that nonlinear multi-dimensional lattice waves subjected to intersite and external on-site potentials are found to be governed by (N+1)-dimensional nonlinear Schrödinger (NLS) equation. In particular, the resonant mode interaction of (2+1)-dimensional NLS equation has been identified and the theory allows the inclusion of transverse effect. We apply the exponential function method to the (2+1)-dimensional NLS equation and obtain the class of soliton solutions with a purely algebraic computational method. Notably, we discuss in detail the effects of the external on-site potentials on the explicit form of the soliton solution generated recursively. Under the action of the external on-site potentials, the model presents a rich variety of oscillating multidromion patterns propagating in the system.
Keywords:  solitons      partial differential equations      lattice dynamics      exact solutions
Received:  20 June 2013      Revised:  12 August 2013      Accepted manuscript online:
 PACS: 03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations) 02.60.Lj (Ordinary and partial differential equations; boundary value problems) 04.20.Jb (Exact solutions)
Corresponding Authors:  L. Kavitha     E-mail:  louiskavitha@yahoo.co.in

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