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Nonlinear Schroedinger equation in three spatial variables

I.V. Alimenkov 1
1Samara State Aerospace University named after academician S.P. Korolev 


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Pages: 55-59.

Abstract:
Smooth analytical solutions are found for the nonlinear Schrödinger equation in the form of solitary waves for the case of three spatial variables. The phenomenon of optical self-focusing is considered.

Keywords:
Schroedinger equation, optical self-focusing.

Citation:
Alimenkov, IV. Nonlinear Schroedinger equation in three spatial variables. Computer Optics 2005; 28: 55-59.

References:
  1. Takhtadzhyan LA, Faddeev LD. The Hamiltonian method in the theory of solitons [In Russian]. Moscow: Nauka Publisher, 1986. 
  2. Dodd RK, Morris HC, Eilbeck JC, Gibbon JD. Soliton and nonlinear wave equations. London, New York: Academic Press Inc; 1982. 
  3. Newell AC. Solitons in mathematics and physics. Philadelphia, PA: Society for Industrial and Applied Mathematics; 1985. 
  4. Rajaraman R. Solitons and instantons: An introduction to solitons and instantons in quantum field theory. New York: Elsevier Science BV; 1982. 
  5. Stepanov VV. Course of differential equations. Moscow: State Publishing House of Technical and Theoretical Literature; 1953. 
  6. Landau LD, Lifshitz EM. Electrodynamics of continuous media. 2nd ed. Oxford: Pergamon Press Ltd; 1984. 
  7. Alimenkov IV. Exactly solvable mathematical models in nonlinear optics. Computer Optics 2005; 28: 45-54.

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