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On nonclassical symmetries of generalized Huxley equations
contribution to the Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (4 - 10 June 2010, Protaras, Cyprus)
2010/11/10
Nonclassical symmetries of a class of generalized Huxley equations of form $u_t=u_{xx}+k(x)u^2(1-u)$ are found. More precisely, for the class under consideration we completely classify reduction opera...
Azimuthons in weakly nonlinear waveguides of different symmetries
Pattern Formation and Solitons (nlin.PS) Optics (physics.optics)
2010/11/10
We show that weakly guiding nonlinear waveguides support stable propagation of rotating spatial solitons (azimuthons). We investigate the role of waveguide symmetry on the soliton rotation. We find th...
Integrability Test for Discrete Equations via Generalized Symmetries
Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/10
In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations c...
While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems.