Classification of solitary wave bifurcations in generalized nonlinear Schrödinger equations

Details Classification of solitary wave bifurcations in generalized nonlinear Schrödinger equations Classification of solitary wave bifurcations in generalized nonlinear Schrödinger equations

2012-03-23

arxiv.org/abs/1203.5148v1

Nonlinear Sciences

Pattern Formation and Solitons

26 pages, 6 figures; to appear in Stud. Appl. Math

Scientific paper

Bifurcations of solitary waves are classified for the generalized nonlinear Schr\"odinger equations with arbitrary nonlinearities and external potentials in arbitrary spatial dimensions. Analytical conditions are derived for three major types of solitary wave bifurcations, namely saddle-node bifurcations, pitchfork bifurcations and transcritical bifurcations. Shapes of power diagrams near these bifurcations are also obtained. It is shown that for pitchfork and transcritical bifurcations, their power diagrams look differently from their familiar solution-bifurcation diagrams. Numerical examples for these three types of bifurcations are given as well. Of these numerical examples, one shows a transcritical bifurcation, which is the first report of transcritical bifurcations in the generalized nonlinear Schr\"odinger equations. Another shows a power loop phenomenon which contains several saddle-node bifurcations, and a third example shows double pitchfork bifurcations. These numerical examples are in good agreement with the analytical results.

Affiliated with

Also associated with

No associations

Rating

Classification of solitary wave bifurcations in generalized nonlinear Schrödinger equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classification of solitary wave bifurcations in generalized nonlinear Schrödinger equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classification of solitary wave bifurcations in generalized nonlinear Schrödinger equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-471478