How Much For The Gina Bmw

mathematical means ...

This is an autobiographical post. So, dear reader, I warn you to flee now that you're on time or stay tuned and Pegaditas the seat because you're going to read you will leave, at least, puzzled.

The story goes back to the days immediately after my PhD in physics, back in late 1996. At that time, I decided to abandon the research that had continued throughout my doctoral thesis: the study of the behavior of light in structures called optical waveguides . Around the same time current was a very promising field of research: the solitons . And I threw myself fully to explore this new world. I looked for support in my research group and tried to convince people to reorient the work of the group to which it seemed to me the immediate future of telecommunications. I did not, but I did not broke down or got discouraged. Rather the contrary. Instead of bringing me to my friends with me, I turned away from them and I went solo. When I put something between the eyes, step over almost everything. Of course, without blood.

started from scratch, because I knew absolutely nothing about the subject of optical solitons, a very small field in the vast ocean of solitons, in general, and this phenomenon is known in fields as diverse as fluid mechanics, astrophysics (thought quite justifiably that the Great Red Spot on Jupiter's atmosphere is a special type of soliton known as Rossby wave ), acoustics, etc. Overalls I spent two years studying and reading books and articles in leading scientific journals. And when those endless ended two years, began arriving in the coveted fruit of the effort and sacrifice alone that I conducted.

But let the issue. What was that work that I undertook in 1997 and lasted until 2004, when I decided to leave again? Well, neither more nor less than to study and try to find a very special kind of exact solutions of a very specific equations called nonlinear Schrödinger equations . Yes, the same kind of equation that appears in quantum mechanics, but now modified so that was no longer linear. The nonlinear Schrödinger equation (NLSE) describes mathematically the propagation of optical pulses (laser) optical fiber, provided and when the width of these pulses is in the range of picoseconds (billionths of a second).

NLSE presents solutions

This so-called "bright soliton" when the sign of the coefficient that accompanies the end of the second-order dispersion (temporal second derivative in the equation) is negative (anomalous dispersion zone), as it is said that has solutions "dark soliton" when the sign is positive (normal dispersion area).

bright solitons tend to take the mathematical form of a hyperbolic secant function and dark solitons of hyperbolic tangent. When the minimum of this function falls to zero is called black soliton, "leaving the name" soliton gray for the remaining cases. Under certain conditions, they also receive all the generic name of "solitary waves."

There are also generalized versions of the equation NLSE, depending on the appearance of certain physical phenomena, more or less complex, which will not comment here in order not to bore the personal. When taking into account such phenomena is necessary to add corrective terms to the equation, such as higher-order dispersion (third derivative and fourth with respect to time) or nonlinear power-law type, for example, among others. The fact is that the equation that results in all cases it is extremely difficult to manage from an analytical point of view and find exact solutions of the same becomes a really exciting adventure. At least for me. And to this I devoted myself for almost 7 years of my life, using a simple technique called "amplitude-coupled phase." Was basically separated by factoring in spatial and temporal dependencies of the solution function of NLS type equation.

Why are so important these soliton-like solutions? Because from them you can set the conditions under which a light pulse propagates undistorted along a nonlinear material medium. And if the distortion does not affect the pulse, systems such as amplifiers and digital signal repeaters are totally unnecessary. There has been transmitted solitons in optical fibers at distances of millions of kilometers, returning them back almost intact, with little experience attenuation (loss of signal strength) and dispersion (pulse broadening).

As I told above, I spent seven years virtually alone (except for some collaborations sporadic), with everything that entails from the point of view not only scientific but also psychological. I had to solve many transcendent questions by email, did not have subsidized projects who attend conferences and meet colleagues, the articles submitted to scientific journals ran one hundred percent of my account, the "fights" with the "referees" I burned slowly and, thus, finally, disgusted and disappointed by how to proceed in some very intolerant, I decided to leave. The results were expressed in a dozen "papers" to prove that I too was once a researcher ... and mathematical means.

Epilogue .- By the way, if you pique my curiosity, and among you there is any future researcher interested in the field of solitons, here are the references of my work. So enjoy!

1. A simple way to show That dog bright femtosecond solitons propagate in Both dispersion regions of an optical fiber ( Journal of Nonlinear Optical Physics & Materials, 1999 ).
2. Dark solitary waves in the nonlinear Schrödinger equation with third order dispersion, self-steepening, and self-frequency shift ( Physical Review E, 1999 ).
3. Bright and dark solitary waves in both dispersion regions of an optical fibre ( Journal of Modern Optics, 2000 ).
4. Black optical solitons for media with parabolic nonlinearity law in the presence of fourth order dispersion ( Optics Communications, 2000 ).
5. Bright solitary waves in high dispersive media with parabolic nonlinearity law: the influence of third order dispersion ( Journal of Modern Optics, 2001 ).
6. Cusp solitons in the cubic quintic nonlinear Schrödinger equation ( Journal of Nonlinear Optical Physics & Materials, 2001 ).
7. An alternative set of bright and dark soliton solutions of the nonlinear Schrödinger equation ( Journal of Nonlinear Optical Physics & Materials, 2001 ).
8. Solution of nonlinear wave equations of the complex quintic Ginzburg-Landau and nonlinear Schrödinger type ( IEEE Photonics Technology Letters, 2002 ).
9. An explicit calculation of the dispersive and nonlinear frequency chirps for femtosecond optical pulses of the high dispersive cubic and cubic-quintic nonlinear Schrödinger equations ( Journal of Nonlinear Optical Physics & Materials, 2002 ).
10. Method for generating solitons sustained by competing nonlinearities by use of optical rectification ( Optics Letters, 2002 ).
11. Optical solitons in highly dispersive media with a dual-power nonlinearity law ( Journal of Optics A: Pure and Applied Optics, 2003 ).
12. Two simple ansätze for obtaining exact solutions of high dispersive nonlinear Schrödinger equations ( Chaos, Solitons, and Fractals, 2004 ).

P.D. Esta entrada forma parte de la Edición 2.1 del Carnaval de Matemáticas (First Anniversary), hosted by Tito Eliatron Dixit.