In this paper, fractional complex transform (FCT) with help of variational iteration method (VIM) is used to obtain numerical and analytical solutions for the fractional Zakharov–Kuznetsov equations. Fractional complex transform (FCT) is proposed to convert fractional Zakharov– Kuznetsov equations to its differential partner and then applied VIM to the new obtained equations. Several examples a...

Weakly nonlinear focusing of quasi-planar ultrasound in a liquid nonuniformly containing many spherical microbubbles is theoretically investigated with special focus on thermal conduction at the bubble-liquid interface toward medical applications such as tumor coagulation by HIFU. Based previously derived Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation our group (Kanagawa, J. Acoust. Soc. Am., 1...

We analyze the behavior of third-order-in-time linear and nonlinear sound waves in thermally relaxing fluids gases as diffusivity vanishes. The acoustic propagation is modeled by Jordan--Moore--Gibson--Thompson equation both its Westervelt-type Kuznetsov-type forms, that is, including general nonlinearities quadratic type. As it turns out, sufficiently smooth solutions these equations converge ...