Coupled Dispersionless and Generalized Heisenberg Ferromagnet Equations\n with Self-Consistent Sources: Geometry and Equivalence

2019/01/05 by Guldana Bekova, Bekova, Guldana, Gulgassyl Nugmanova +7
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1901.01470

openalex publication_date 2019/01/05 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

Abstract

We propose a new integrable coupled dispersionless equation with\nself-consistent sources (CDESCS). We obtain the Lax pair and the equivalent\ngeneralized Heisenberg ferromagnet equation (GHFE), demonstrating its\nintegrability. Specifically, we explore the geometry of these equations. Last,\nwe consider the relation between the motion of curves/surfaces and the CDESCS\nand the GHFE.\n

Citations

• Integrability of the Gauss-Codazzi-Mainardi equation in 2+1 dimensions
• Soliton and Periodic solutions of the Short Pulse Model Equation
• The Short Pulse Equation Is Integrable
• Propagation of ultra-short optical pulses in cubic nonlinear media
• Solitary wave solutions of the short pulse equation
• Geometric formulation and multi-dark soliton solution to the defocusinig complex short pulse equation
• New Reductions of a Matrix Generalized Heisenberg Ferromagnet Equation
• Integrable Flows of Curves/Surfaces, Generalized Heisenberg Ferromagnet Equation and Complex Coupled Dispersionless Equation

Related

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• Camassa-Holm and M-CIV equations with self-consistent sources: geometry and peakon solutions
• Integrable Flows of Curves/Surfaces, Generalized Heisenberg Ferromagnet Equation and Complex Coupled Dispersionless Equation
• Dispersionless Limits of Integrable Generalized Heisenberg Ferromagnet Equations
• Notes on Integrable Motion of Two Interacting Curves and Two-layer Generalized Heisenberg Ferromagnet Equations