1Ecole Nationale Supérieure Polytechnique, University of Yaounde I, PO Box 8390, Cameroon2Department of Physics, Faculty of Science, University of Yaounde I, PO Box. 812, Cameroon3The Abdus Salam International Centre for Theoretical Physics, PO Box 586, Strada Costiera, II-34014, Trieste, Italy
Dynamical System Approach to a Coupled Dispersionless System: Localized and Periodic Traveling Waves
1Ecole Nationale Supérieure Polytechnique, University of Yaounde I, PO Box 8390, Cameroon2Department of Physics, Faculty of Science, University of Yaounde I, PO Box. 812, Cameroon3The Abdus Salam International Centre for Theoretical Physics, PO Box 586, Strada Costiera, II-34014, Trieste, Italy
摘要We investigate the dynamical behavior of a coupled dispersionless system describing a current-conducting string with infinite length within a magnetic field. Thus, following a dynamical system approach, we unwrap typical miscellaneous traveling waves including localized and periodic ones. Studying the relative stabilities of such structures through their energy densities, we find that under some boundary conditions, localized waves moving in positive directions are more stable than periodic waves which in contrast stand for the most stable traveling waves in another boundary condition situation.
Abstract：We investigate the dynamical behavior of a coupled dispersionless system describing a current-conducting string with infinite length within a magnetic field. Thus, following a dynamical system approach, we unwrap typical miscellaneous traveling waves including localized and periodic ones. Studying the relative stabilities of such structures through their energy densities, we find that under some boundary conditions, localized waves moving in positive directions are more stable than periodic waves which in contrast stand for the most stable traveling waves in another boundary condition situation.
[1] Konno K and Kakuhata H 1996 J. Phys. Soc. Jpn. 65 340 [2] Kakuhata H and Konno K 1997 J. Phys. A: Math. Gen. 30 L401 [3] Kakuhata H and Konno K 2002 Theor. Math. Phys. 133 1675 [4] Drazin P G and Johnson R S 1989 Solitons: anIntroduction (Cambridge: Cambridge University) [5] Ablowitz M J and Clarkson P A 1991 Solitons,Nonlinear Evolution Equations and Inverse Scattering (Cambridge:Cambridge University) [6] Dirac P A M 1964 Lectures on Quantum Mechanic (NewYork: Belfer Graduate School of Science, Yeshiva University) [7] Kakuhata H and Konno K 1996 J. Phys. Soc. Jpn. 65 1 [8] Gradshteyn I S and Ryzhik I M 2000 Table ofIntegrals, Series, and Products (New York: Academic)
2009, Vol. 26 
