Integrable two-dimensional Lorentz-invariant nonlinear model of a complex scalar field (complex sine-Gordon II)

A study is made of the new two-dimensional nonlinear model of a complex scalar field (“complex sine-Gordon II”) which was discovered earlier by the author and can be integrated by the inverse scattering technique. The corresponding linear spectral problem is found and formulated in terms of the matrices of the algebra of the group $SU(3)$. The model has two types of soliton solutions which have vanishing and nonvanishing asymptotic behavior at infinity. An infinite series of integrable Lorentz-invariant systems that generalize the sine-Gordon equation is also obtained; when the first of them is reduced to Lagrangian form, it is identical with the model studied in the present paper.