{"title":"Instability of Soliton Solutions to the Schamel-nonlinear Schr\u00f6dinger Equation","authors":"Sarun Phibanchon, Michael A. Allen","volume":61,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":18,"pagesEnd":21,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10680","abstract":"
A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schr\u252c¿odinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton.<\/p>\r\n","references":"[1] E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos,\r\n2nd ed. Cambridge: Cambridge University Press, 2000.\r\n[2] H. Washimi and T. Taniuti, \"Propagation of ion-acoustic solitary waves\r\nof small amplitude,\" Phys. Rev. Lett., vol. 17, pp. 996-8, 1966.\r\n[3] H. Schamel, \"Stationary solitary, snoidal and sinusoidal ion acoustic\r\nwaves,\" Plasma Phys., vol. 14, no. 10, pp. 905-24, 1972.\r\n[4] G. P. Agrawal, Nonlinear Fiber Optics. New York: Academic Press,\r\n2001.\r\n[5] R. K. Bullough, P. M. Jack, P. W. Kitchenside, and R. Saunders,\r\n\"Solitons in laser physics,\" Phys. Scr., vol. 20, pp. 364-381, 1979.\r\n[6] R. Fedele, H. Schamel, and P. K. Shukla, \"Solitons in the Madelung-s\r\nfluid,\" Phys. Scr., vol. T98, pp. 18-23, 2002.\r\n[7] S. Phibanchon and M. A. Allen, \"Numerical solutions of the nonlinear\r\nSchr\u252c\u00bfodinger equation with a square root nonlinearity,\" in The 2010\r\nInternational Conference on Computational Science and its Applications\r\n(ICCSA 2010). Los Alamitos, CA, USA: IEEE Computer Society, 2010,\r\npp. 293-5.\r\n[8] G. Rowlands, \"Stability of nonlinear plasma waves,\" J. Plasma Phys.,\r\nvol. 3, pp. 567-76, 1969.\r\n[9] D. Anderson, M. Lisak, and A. Berntson, \"A variational approach to\r\nnonlinear evolution equations in optics,\" Pramana J. Phys., vol. 57, pp.\r\n917-36, 2001.\r\n[10] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,\r\nNumerical Recipes in C, 2nd ed. Cambridge: Cambridge University\r\nPress, 1992.\r\n[11] P. Frycz and E. Infeld, \"Spontaneous transition from flat to cylindrical\r\nsolitons,\" Phys. Rev. Lett., vol. 63, no. 4, pp. 384-5, 1989.\r\n[12] S. Phibanchon and M. A. Allen, \"Time evolution of perturbed solitons of\r\nmodified Kadomtsev-Petviashvili equations,\" in The 2007 International\r\nConference on Computational Science and its Applications (ICCSA\r\n2007). Los Alamitos, CA, USA: IEEE Computer Society, 2007, pp.\r\n20-3.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 61, 2012"}