Dynamics of two-dimensional solitons in weakly dispersive media

The Cauchy Problem and Stability of Solitary-Wave Solutions for RLW–KP-Type Equations

“…In this case, for e ¼ À1 and for any integer p; (1.1) possesses nontrivial solitary-wave solutions (see [15]). These were observed numerically for p ¼ 1 and e ¼ À1 in [25].…”

“…Several of the technical points in the proof of the instability in [41] were carried out in detail in [14]. When e ¼ À1 and L ¼ À@ is the regularized version of a two-dimensional fifth-order KdV-type equation introduced by Abramyan and Stepanyants [2] and Karpman and Belashov [25]. In this case, for e ¼ À1 and for any integer p; (1.1) possesses nontrivial solitary-wave solutions (see [15]).…”

Dynamics of IGW and traveling ionospheric disturbances in regions with sharp gradients of the ionospheric parameters

“…The obtained equation is the generalization of the Kadomtsev-Petviashvili equation (so-called BelashovKarpman (BK) equation), for the first time it has been obtained in , Karpman and Belashov (1991) and investigated in detail in a number of works (see Belashov and Vladimirov, 2005). It is written here for the velocity of the neutral component at the heights of the F-region with @ z ¼ 0 without dissipation and describes the nonlinear IGW solitons and nonlinear wave packets, with the structure determined by both the coefficients and the function u(0, n, y) corresponding to the initial condition, i.e., it depends on the sort of perturbation and accordingly the type of the source as well.…”

The Cauchy Problem for Higher-Order KP Equations

“…We shall denote by J the integral in the left-hand side of (15). We shall divide the domain of integration taking into account which term dominates in the left-hand side of (17).…”

“…Such equations occur naturally in the modeling of certain long dispersive waves (cf. [2,15,16]). The study of their solitary wave solutions was done in [6,7].…”