Lax pair, Darboux Transformations and solitonic solutions for a (2+1) dimensional NLSE
P. G. Estevez, G.A. Hern\'aez (Universidad de Salamanca, SPAIN)
TL;DR
This paper derives the Lax pair, Darboux transformations, and solitonic solutions for a (2+1)-dimensional nonlinear Schrödinger equation using the Singular Manifold Method, enabling iterative construction of soliton solutions.
Contribution
It introduces a novel application of the Singular Manifold Method to derive integrability structures and soliton solutions for a higher-dimensional NLSE.
Findings
Derived Lax pair and Darboux transformations for the 2+1D NLSE
Constructed tau functions enabling soliton solution generation
Demonstrated iterative soliton solution building
Abstract
In this paper the Singular Manifold Method has allowed us to obtain the Lax pair, Darboux transformations and tau functions for a non-linear Schr\"odiger equation in 2+1 dimensions. In this way we can iteratively build different kind of solutions with solitonic behavior.
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Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Nonlinear Photonic Systems