Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

A Class of Integrable Nonlinear Evolution Equations Driven Exclusively by Extrinsic Quadratic Effects

Document Type : Original Article

Author
Anouchah Latifi
Qom University of Technology
10.30511/ttmp.2025.2053029.1046
Abstract
In this work, we investigate a class of integrable nonlinear evolution equations where extrinsic quadratic contributions are the only source of nonlinearity. Within the Inverse Scattering Transform (IST) framework and using the D-bar method based on the Riemann-Hilbert approach, we extend the analysis to systems governed purely by singular dispersion relations, and we derive integrable equations that lack intrinsic nonlinearities and are driven only by the interaction between the evolution equations and their spectral problems. By suitable choices of singular dispersion relations, we derive the "truncated" Nonlinear Schrodinger (NLS) and Korteweg-de Vries (KdV) Equations that exhibit localized coherent structures and singular asymptotic behaviors that arise independently of initial conditions. The integrability of these systems is confirmed through their associated Lax pairs. To demonstrate the physical relevance of these systems, we derive them in the context of laser-plasma interactions, where they model the formation of propagating localized structures and energy transfer dynamics.
Keywords
Integrability
extrinsic nonlinearity
Lax pair
nonlinear coupling
singular dispersion relation
Subjects
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Transactions in Theoretical and Mathematical Physics
Volume 2, Issue 1
Winter 2025
Pages 8-21

  • Receive Date 09 February 2025
  • Accept Date 25 February 2025
  • First Publish Date 25 February 2025
  • Publish Date 01 February 2025