Exactly solvable Wadati potentials in the PT-symmetric Gross-Pitaevskii equation
I. V. Barashenkov, D. A. Zezyulin, and V. V. Konotop
TL;DR
This paper develops a method to construct exactly solvable PT-symmetric Wadati potentials in the Gross-Pitaevskii equation, enabling the derivation of various localized solutions such as bright and dark solitons.
Contribution
It introduces a systematic recipe for building Wadati potentials that support exact localized solutions in PT-symmetric Gross-Pitaevskii equations.
Findings
Constructed explicit Wadati potentials supporting solitons.
Derived bright and dark soliton solutions.
Provided a general framework for exact solutions in PT-symmetric systems.
Abstract
This note examines Gross-Pitaevskii equations with PT-symmetric potentials of the Wadati type: . We formulate a recipe for the construction of Wadati potentials supporting exact localised solutions. The general procedure is exemplified by equations with attractive and repulsive cubic nonlinearity bearing a variety of bright and dark solitons.
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