New solutions in the theory of self-focusing with saturating nonlinearity

Kovalev, V.; Popov, K.; Bychenkov, V.
January 2012
Journal of Experimental & Theoretical Physics;Jan2012, Vol. 114 Issue 1, p25
Academic Journal
On the basis of an approximate analytic solution of a Cauchy problem for a nonlinear Schrödinger (NLS) equation describing steady-state light beams in a medium with saturating nonlinearity by the method of renormgroup (RG) symmetries, a classification of self-focusing solutions is given depending on two control parameters: the relative contributions of diffraction and nonlinearity and the saturation strength of the nonlinearity. The existence of tube-type self-focusing solutions is proved for an entering beam with Gaussian radial distribution of intensity. Numerical simulation is carried out that allows one to verify the theory developed and to determine its applicability limits.


Related Articles

  • Real analytic quasi-periodic solutions for the derivative nonlinear Schrödinger equations. Geng, Jiansheng; Wu, Jian // Journal of Mathematical Physics;Oct2012, Vol. 53 Issue 10, p102702 

    In this paper, we show that one dimension derivative nonlinear Schrödinger equation admits a whitney smooth family of small amplitude, real analytic quasi-periodic solutions with two Diophantine frequencies. The proof is based on a partial Birkhoff normal form reduction and an abstract...

  • Analytic plane wave solutions for the quaternionic potential step. De Leo, Stefano; Ducati, Gisele C.; Madureira, Tiago M. // Journal of Mathematical Physics;Aug2006, Vol. 47 Issue 8, p082106 

    By using the recent mathematical tools developed in quaternionic differential operator theory, we solve the Schrödinger equation in the presence of a quaternionic step potential. The analytic solution for the stationary states allows one to explicitly show the qualitative and quantitative...

  • Repelling, Delay, and Polarization for Soliton Collisions in the CNLSE. Sonnier, W. J. // AIP Conference Proceedings;11/30/2011, Vol. 1404 Issue 1, p77 

    The system of coupled nonlinear Schrödinger's equations (CNLSE) is solved numerically by means of a conservative difference scheme. Values of the cross-modulation parameter, α2, are chosen to induce collisions for which the initial profiles are eventually reversed, focusing on two specific...

  • Propagation properties of a sinh-Gaussian beam in a Kerr medium. Chen, R.; Zheng, H.; Chu, X. // Applied Physics B: Lasers & Optics;Mar2011, Vol. 102 Issue 3, p695 

    The effect of the Kerr nonlinearity on a sinh-Gaussian beam is investigated by using the nonlinear Schrödinger equation (NLS). Based on the method of moments, the evolution of the sinh-Gaussian beam width in the root-mean-square (RMS) sense is analytically described. Numerical simulations...

  • Quasiperiodic solutions for matrix nonlinear Schrödinger equations. Wisse, M. A. // Journal of Mathematical Physics;Nov92, Vol. 33 Issue 11, p3694 

    The Adler–Kostant–Symes theorem yields isospectral Hamiltonian flows on the dual [larger_closed_square]erm>$$g+* of a Lie subalgebra [larger_closed_square]erm>$$g+ of a loop algebra [larger_closed_square]erm>$$g. A general approach relating the method of integration of Krichever,...

  • Modified nonlinear Schrodinger equation: Spectral... Doktorov, E.V.; Shchesnovich, V.S. // Journal of Mathematical Physics;Dec95, Vol. 36 Issue 12, p7009 

    Studies the modified nonlinear Schrodinger (MNLS) equation. Gauge equivalence to one which is canonical in the class of nonlinear equations associated with the quadratic bundle; Expression for the N-soliton solution of the MNLS equation; Spectral transform matrix for both continuous and...

  • Weak collapse in the nonlinear Schrödinger equation. Ovchinnikov, Yu. N. // JETP Letters;3/10/99, Vol. 69 Issue 5, p418 

    It is shown that there exists a three-parameter family of exact solutions of the nonlinear Schrödinger equation that lead to weak collapse.

  • Quadratic Spline Approximation Solution of the Generalized Nonlinear Schrödinger Equation. Al-Said, E. A.; Hassan, Saleh M. // Global Journal of Pure & Applied Mathematics;2011, Vol. 7 Issue 3, p307 

    Here we develop a finite difference method to obtain approximatesolutions of the generalized nonlinear Schrödingerequation (GNLS). The numerical method is derived through thesemidiscretization and application of the quadratic splineapproximation. Neumann boundary conditions are considered in...

  • NUMERICAL SIMULATIONS OF YARN UNWINDING FROM PACKAGES.  // Mathematical & Computational Applications;2010 Special Issue, Vol. 15 Issue 4, p846 

    No abstract available.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics