{"title":"Two-Dimensional Solitary Wave Solution to the Quadratic Nonlinear Schrdinger Equation","authors":"Sarun Phibanchon","volume":73,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":149,"pagesEnd":152,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/5505","abstract":"
The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.<\/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] G. P. Agrawal, Nonlinear Fiber Optics. New York: Academic Press,\r\n2001.\r\n[4] A. Biswas and S. Konar, Introduction to non-Kerr Law Optical Solitons.\r\nBoca Raton: Chapman and Hall, 2007.\r\n[5] 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[6] H. Schamel, \"Stationary solitary, snoidal and sinusoidal ion acoustic\r\nwaves,\" Plasma Phys., vol. 14, no. 10, pp. 905-24, 1972.\r\n[7] \u00d4\u00c7\u00f6\u00d4\u00c7\u00f6, \"A modified Korteweg-de Vries equation for ion acoustic waves\r\ndue to resonant electrons,\" J. Plasma Phys., vol. 9, no. 3, pp. 377-87,\r\n1973.\r\n[8] V. I. Petviashvili, \"Equation of an extraordinary soliton,\" Sov. J. Plasma\r\nPhys., vol. 2, no. 3, pp. 257-8, 1976.\r\n[9] D. E. Pelinovsky and Y. A. Stepanyants, \"Convergence of Petviashvili-s\r\niteration method for numerical approximation of stationary solutions of\r\nnonlinear wave equations,\" SIAM J. Numer. Anal., vol. 42, no. 3, pp.\r\n1110-1127, 2004.\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.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 73, 2013"}