Solutions of the modified Ostrovskii equation with cubic non-linearity

✍ Scribed by S.P Nikitenkova; Yu.A Stepanyants; L.M Chikhladze

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 572 KB
• Volume: 64
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(00)00048-4

✦ Synopsis

Approximate solutions of the stationary Ostrovskii equation [1] with cubic non-linearity, describing, in particular, wave processes in rotating media, are constructed. A new integral invariant of this equation is found, making it possible to dose the system of approximate equations and to eliminate excessive arbitrariness in the parameters. It is shown that there is a family of periodic stationary solutions in the form of a combination of a sawtooth wave with smoothed peaks and troughs, in which there are solitons of the modified Korteveg-de Vries equation of different polarity. This family of solutions is well described by approximate analytical theory, in which the role of a perturbation is essentially played by the ratio of the characteristic size of the soliton to the period of the sawtooth wave. The analytical solutions constructed are in good agreement with numerical solutions. The use of such solutions as the starting data for numerical calculations within the framework of the non-stationary equation has made it possible to establish the degree to which they are stationary and their stability to small perturbations.