Tri-Integrable Couplings of the Giachetti-Johnson Soliton Hierarchy as well as Their Hamiltonian Structure

Lei Wang,Ya-Ning Tang

doi:10.1155/2014/627924

Abstract

Based on zero curvature equations from semidirect sums of Lie algebras, we construct tri-integrable couplings of the Giachetti-Johnson (GJ) hierarchy of soliton equations and establish Hamiltonian structures of the resulting tri-integrable couplings by the variational identity.

Highlights

Soliton theory is a power tool in expanding and describing the nonlinear phenomena in the fields of nonlinear optics, plasma physics, magnetic fluid, and so on
Tri-integrable couplings for the GiachettiJohnson hierarchy of continuous soliton equations were generated by using semidirect sums of Lie algebras
We established their Hamiltonian structures through the variational identities

Summary

Introduction

Soliton theory is a power tool in expanding and describing the nonlinear phenomena in the fields of nonlinear optics, plasma physics, magnetic fluid, and so on. We hope to generate the Hamiltonian structure of the resulting triintegrable couplings. We will show that the resulting tri-integrable couplings have a recursion relation. 2. Tri-Integrable Couplings of the Giachetti-Johnson (GJ) Hierarchy U = (r) , s and choosing the initial data a0 = −1, b0 = c0 = 0, the stationary zero curvature equation Wx = [U, W] generates bi+1

Results

Conclusion