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Generalizations of the short pulse equation.
Andrew N W Hone1, Vladimir Novikov2, Jing Ping Wang1
11School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7FS UK.
Letters in Mathematical Physics
|April 3, 2018
Summary
This study classifies second-order polynomial partial differential equations. These equations generalize the well-known short pulse equation, advancing the field of integrable systems.
Area of Science:
- Mathematical Physics
- Nonlinear Dynamics
Background:
- The short pulse equation is a significant model in nonlinear optics and fluid dynamics.
- Classifying integrable partial differential equations (PDEs) is crucial for understanding their properties and applications.
Purpose of the Study:
- To classify integrable scalar polynomial partial differential equations of second order.
- To generalize the existing classification to include equations beyond the standard short pulse equation.
Main Methods:
- Employing techniques from the theory of integrable systems.
- Utilizing algebraic and geometric methods for classifying polynomial PDEs.
Main Results:
- A comprehensive classification of a new family of integrable second-order scalar polynomial PDEs.
- Identification of generalizations of the short pulse equation within this new class.
Conclusions:
- The classification provides a deeper understanding of integrable nonlinear PDEs.
- This work expands the toolkit for analyzing complex nonlinear phenomena described by such equations.
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