Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Korteweg–de Vries equations | Statement: [Bourgain spaces, appliedTo, Korteweg–de Vries equations]

Target entity: Korteweg–de Vries equations
Context triple: [Bourgain spaces, appliedTo, Korteweg–de Vries equations]

• A. Korteweg–De Vries equation chosen
  The Korteweg–De Vries equation is a fundamental nonlinear partial differential equation that models shallow water waves and solitons, playing a central role in the theory of integrable systems.
• B. Kadomtsev–Petviashvili equation
  The Kadomtsev–Petviashvili equation is a fundamental nonlinear partial differential equation in mathematical physics that generalizes the Korteweg–De Vries equation to two spatial dimensions to describe the evolution of weakly dispersive, weakly nonlinear waves.
• C. Gardner–Greene–Kruskal–Miura paper on the KdV equation
  The Gardner–Greene–Kruskal–Miura paper on the KdV equation is a landmark work in mathematical physics that introduced the inverse scattering transform and revealed the integrable, soliton-bearing nature of the Korteweg–de Vries equation.
• D. Zur Theorie der nichtlinearen Wellen
  "Zur Theorie der nichtlinearen Wellen" is Klaus Hasselmann's doctoral thesis, a foundational work on the behavior and mathematical description of nonlinear waves in physics.
• E. Painlevé–Kruskal theorem
  The Painlevé–Kruskal theorem is a result in the theory of nonlinear differential equations that characterizes integrability through the analytic structure of their solutions, particularly via the Painlevé property.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.