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Soliton pair interaction law in parametrically driven Newtonian fluid.

M G Clerc¹, S Coulibaly, N Mujica

¹Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile. marcel@dfi.uchile.cl

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|July 22, 2009

Summary

Localized excitations in water exhibit predictable interactions near Faraday instability. Experimental results closely match the theoretical pair interaction law derived from a nonlinear Schrödinger model.

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Area of Science:

Fluid dynamics
Nonlinear physics
Wave phenomena

Background:

Vertically driven water containers exhibit complex localized excitations.
Faraday instability is a key phenomenon in parametrically driven systems.
Understanding localized excitation interactions is crucial in nonlinear dynamics.

Purpose of the Study:

To experimentally and theoretically investigate the motion and interaction of localized excitations.
To model the system using the parametrically driven damped nonlinear Schrödinger equation.
To characterize the pair interaction law between localized excitations.

Main Methods:

Experimental study of localized excitations in a vertically driven rectangular water container.
Theoretical modeling using the nonlinear Schrödinger equation.
Comparison of experimental data with the derived pair interaction law.

Main Results:

The parametrically driven damped nonlinear Schrödinger equation effectively models the system.
A specific pair interaction law for localized excitations was characterized.
Experimental observations showed good agreement with the theoretical interaction law.

Conclusions:

The study successfully links experimental observations with theoretical predictions.
The nonlinear Schrödinger model provides a valid framework for understanding these interactions.
The characterized pair interaction law is experimentally validated.