Matrix generalisation of the modified Korteweg-de Vries equation
F A KhalilovInst. for Low Temp. Phys. & Eng., Acad. of Sci., Kharkov, Ukrainian SSR, USSRE. Ya. KhruslovInst. for Low Temp. Phys. & Eng., Acad. of Sci., Kharkov, Ukrainian SSR, USSR
1990en
ABI
Abstract
The matrix-modified Korteweg-de Vries equation (MMKdV) Phi t+3( Phi , Phi xx)-6 Phi Phi x Phi + Phi xxx=0 is studied by means of the inverse scattering problem. The Lax L-A pair is found; the direct and the inverse scattering problems for the L-operator are investigated; and the time evolution of the scattering data is traced. The simplest solutions of the MMKdV equation and the infinite series of integrals of motion are constructed.
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