×

Growth rate of transverse instabilities of solitary pulse solutions to a family of modified Zakharov-Kuznetsov equations. (English) Zbl 1220.76080

Summary: Using the small-\(k\) expansion method, we obtain a closed-form expression for the growth rate of long-wavelength transverse instabilities of solitary pulse solutions to a modified Zakharov-Kuznetsov equation with a nonlinearity of the form \((Au^{p}+Bu^{2p})u_{x}\).

MSC:

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q35 PDEs in connection with fluid mechanics
35Q51 Soliton equations
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Infeld, E.; Rowlands, G., Nonlinear Waves, Solitons and Chaos (2000), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0726.76018
[2] Zakharov, V. E.; Kuznetsov, E. A., Sov. Phys. JETP, 39, 285 (1974)
[3] Shukla, P. K.; Bharuthram, R., Phys. Rev. A, 34, 4457 (1986) · Zbl 0602.76117
[4] Das, K. P.; Verheest, F., J. Plasma Phys., 41, 139 (1989)
[5] Verheest, F.; Mace, R. L.; Pillay, S. R.; Hellberg, M. A., J. Phys. A: Math. Gen., 35, 795 (2002)
[6] Duan, W.-S., Europhys. Lett., 66, 192 (2004)
[7] Das, G. C.; Sarma, J.; Gao, Y.-T.; Uberoi, C., Phys. Plasmas, 7, 2374 (2000)
[8] Laedke, E. W.; Spatschek, K. H., J. Plasma Phys., 32, 263 (1984)
[9] Frycz, P.; Infeld, E.; Samson, J. C., Phys. Rev. Lett., 69, 1057 (1992)
[10] Jorge, M. C.; Cruz-Pacheco, G.; Mier-y-Teran-Romero, L.; Smyth, N. F., Chaos, 15, 037104 (2005)
[11] Laedke, E. W.; Spatschek, K. H., J. Plasma Phys., 28, 469 (1982)
[12] M.A. Allen, The evolution of plane solitons, PhD thesis, University of Warwick, 1994; M.A. Allen, The evolution of plane solitons, PhD thesis, University of Warwick, 1994
[13] Munro, S.; Parkes, E. J., J. Plasma Phys., 64, 411 (2000)
[14] J. Uppaman, Stability of solitary wave solutions of the extended Zakharov-Kuznetsov equation, Master’s thesis, Mahidol University, 2007; J. Uppaman, Stability of solitary wave solutions of the extended Zakharov-Kuznetsov equation, Master’s thesis, Mahidol University, 2007
[15] Allen, M. A.; Phibanchon, S.; Rowlands, G., J. Plasma Phys., 73, 215 (2007)
[16] Zhang, W.; Chang, Q.; Jiang, B., Chaos Solitons Fractals, 13, 311 (2002)
[17] Rowlands, G., J. Plasma Phys., 3, 567 (1969)
[18] Allen, M. A.; Rowlands, G., J. Plasma Phys., 50, 413 (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.