Solutions of the modified Ostrovskii equation with cubic nonlinearity (Q2761281)

The authors investigate the Ostrovskii equation [\textit{L. A. Ostrovskii}, Okeanologiya 18, No. 2, 181-191 (1978)] in the dimensionless form NEWLINE\[NEWLINE\Biggl(u_t+ 3u^2u_x- {\sigma\over 4} u_{xxx}\Biggr)_x= {\varepsilon^2\over 2} u,\tag{1}NEWLINE\]NEWLINE where \(\varepsilon\) is dimensionless parameter, \(\sigma\) determines the dispersion type in the short-wave part of the spectrum. This equation corresponds to the cubic nonlinearity case in the description of wave processes in rotating media. A new integral invariant is found for this equation. The properties of the family of periodic stationary solutions to the equation (1) are discussed.