Painlevé Integrability And Shifted Nonlocal Reductions Of A Variable Coefficient Coupled HI Mkdv System
Taylan Demir
TL;DR
This work addresses the integrability of a variable-coefficient HI–mKdV system under shifted nonlocal reductions by applying the Weiss–Tabor–Carnevale Painlevé test to derive coefficient constraints that permit a time reparametrization to an autonomous model. It develops a Hirota bilinear representation and demonstrates that shifted symmetries create new symmetry centers without altering soliton shapes, as shown in a concrete N = 4 → 2 reduction and a shifted-PT one-soliton. The results provide a classification of admissible coefficient profiles and show how to map variable-coefficient solutions back to constant-coefficient HI–mKdV forms, preserving integrability structures such as the Lax pair. The findings illuminate the interplay between nonlocal shifted reductions, PT-symmetry, and non-autonomous dispersion in multi-component integrable systems, with explicit soliton constructions and symmetry-center interpretations.
Abstract
We analyze a variable coefficient coupled HI mKdV system that has shifted nonlocal reductions. The Weiss Tabor Carnevale test gives us coefficient restrictions to perform a time reparametrization to achieve an autonomous integrable model. We also show a Hirota bilinear form along with a simplified example to demonstrate how the shifted symmetries create new symmetry centers, but do not affect the shape of the soliton.