# Integrable Substructure in a Korteweg Capillarity Model. A Karman-Tsien Type Constitutive Relation

@article{Rogers2014IntegrableSI, title={Integrable Substructure in a Korteweg Capillarity Model. A Karman-Tsien Type Constitutive Relation}, author={Colin Rogers}, journal={Journal of Nonlinear Mathematical Physics}, year={2014}, volume={21}, pages={74 - 88} }

A classical Korteweg capillarity system with a Karman-Tsien type (κ, ρ) constitutive relation is shown, via a Madelung transformation and use of invariants of motion, to admit integrable Hamiltonian subsystems.

## 12 Citations

The Korteweg capillarity system. Integrable reduction via gauge and reciprocal links

- Mathematics
- 2016

This classical Korteweg capillarity system is here encapsulated in a quintic derivative nonlinear Schrödinger equation for a model Kármán‐Tsien type capillarity law. An integrable subsystem is…

On the Lagrangian version of the Korteweg capillarity system: integrability aspects

- Mathematics
- 2020

A Lagrangian version of the classical 1+1-dimensional Korteweg capillarity system is shown to encapsulate as a particular reduction an integrable Boussinesq equation. The associated integrability of…

Reciprocal gausson phenomena in a Korteweg capillarity system

- Mathematics, PhysicsMeccanica
- 2019

In previous work in the literature, a kinetic derivation of a logarithmic nonlinear Schrodinger equation incorporating a de Broglie–Bohm term has been obtained in a capillarity context. Here,…

The classical Korteweg capillarity system: geometry and invariant transformations

- Mathematics
- 2014

A class of invariant transformations is presented for the classical Korteweg capillarity system. The invariance is an extension of a kind originally introduced in an anisentropic gasdynamics context.…

Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System

- Mathematics
- 2017

A class of nonlinear Schr\"{o}dinger equations involving a triad of power law terms together with a de Broglie-Bohm potential is shown to admit symmetry reduction to a hybrid Ermakov-Painlev\'{e} II…

On relativistic gasdynamics: invariance under a class of reciprocal-type transformations and integrable Heisenberg spin connections

- PhysicsProceedings of the Royal Society A
- 2020

A classical system of conservation laws descriptive of relativistic gasdynamics is examined. In the two-dimensional stationary case, the system is shown to be invariant under a novel multi-parameter…

Relativistic dissipatons in integrable nonlinear Majorana type spinor model

- Physics
- 2022

By method of moving frame, the relativistic integrable nonlinear model for real, Majorana type spinor fields in 1+1 dimensions is introduced and gauge equivalence of this model with Papanicolau spin…

Ermakov-Painlevé II Reduction in Cold Plasma Physics. Application of a Bäcklund Transformation

- Physics
- 2018

Abstract A class of symmetry transformations of a type originally introduced in a nonlinear optics context is used here to isolate an integrable Ermakov-Painlevé II reduction of a resonant NLS…

On a Novel Resonant Ermakov-NLS System: Painlevé Reduction

- Mathematics, Physics
- 2018

A novel resonant Ermakov-NLS system is introduced which admits symmetry reduction to a hybrid Ermakov-Painleve II system. If the latter is Hamiltonian then combination with a characteristic Ermakov…

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