Solitary waves for a nonlinear dispersive long wave equation

Abstract

All the possible traveling wave solutions of Whitham-Broer-Kaup (WBK) equation are investigated in the present paper. By employing phase plane analysis, transition boundaries are derived to divide the parameter space into several regions associated with different types of phase portraits corresponding to different forms of wave solutions. All the exact expressions of bounded wave solutions are obtained as well as their existence conditions. The mechanism of bifurcation between different waves with varying Hamiltonian value has been revealed. It is pointed out that as the periods of two coexisted periodic waves tend to infinity, they may evolve to two solitary waves. Furthermore, when their trajectories pass through the common saddle point, the two solitary waves may merge into a periodic wave, and its amplitude is nearly equal to the sum of the amplitudes of the two solitary wave solutions.

Doubly periodic patterns of modulated hydrodynamic waves: Exact solutions of the Davey-Stewartson system

“…(22)- (25) and (29)-(32) is striking. Figure 4 shows that the expressions (26)-(32) just constitute an ordinary dark 2-soliton solution (collision of two dark solitons).…”

“…permanent, nonlinear localized modes of dispersive systems, have received tremendous attention both in optics [22,23] and hydrodynamics [24][25][26]. Solitary waves for generalized nonlinear long wave (Whitham-BroerKaup) models [25] and two-layer fluids [26] have been studied intensively. Here we focus on the finite depth fluid configuration, and allow for modulations in two mutually perpendicular, horizontal directions, i.e.…”

Determination of molecular orientation using molecular dynamics for polymer melt flows in circular ducts

“…where l is the extension of macromolecules. The orientation ellipse has been already used to show fiber orientations in fiber suspension flow modeling by some researchers [25][26][27][28][29][30][31][32][33][34]. For instance, Chiba et al developed a model to determine fiber suspension flow through a parallel plate channel.…”