New Solutions of Nonlocal NLS, mKdV and Hirota Equations

2023/06/01 by Avinash Khare, Avadh Saxena, Khare, Avinash +1 · 1 citation
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2306.00329

openalex publication_date 2023/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we provide several novel solutions of the Ablowitz-Musslimani as well Yang's versions of the nonlocal nonlinear Schrödinger (NLS) equation, nonlocal modified Korteweg-de Vries (mKdV) as well as nonlocal Hirota equations. In each case we compare and contrast the corresponding solutions of the relevant local equation. Further, we provide new solutions of the local NLS, local mKdV and local Hirota equations which are not the solutions of the corresponding nonlocal equations.

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• Loop Algebra Splitting and Darboux Transformations for Nonlocal Derivative Nonlinear Schrödinger Hierarchies

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