By B. V. Chirikov (auth.), Professor Fatkulla Abdullaev, Dr. Alan R. Bishop, Dr. Stephanos Pnevmatikos (eds.)
ISBN-10: 3642847749
ISBN-13: 9783642847745
ISBN-10: 3642847765
ISBN-13: 9783642847769
In the previous 3 a long time there was huge, immense growth in opting for the basic position that nonlinearity performs in actual platforms, together with assisting soliton-like options and self-trapped sxcitations resembling polarons. throughout the similar interval, equally striking growth has happened in knowing the results of disease in linear quantum difficulties, particularly relating to Anderson localization bobbing up from impurities, random spatial buildings, stochastic utilized fields, and so on. those notable effects of ailment, noise and nonlinearity often take place jointly in actual structures. but there were purely restricted makes an attempt to increase systematic suggestions which could contain all of those parts, that can make stronger, supplement or frustrate one another. This e-book features a variety of articles which supply vital steps towards the objective of systematic figuring out and class of phenomenology. specialists from Australia, Europe, Japan, united states, and the USSR describe either mathematical and numerical suggestions - specifically from soliton and statistical physics disciplines - and applicaations to a few very important actual structures and units, together with optical and digital transmission strains, liquid crystals, biophysics and magnetism.
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Additional resources for Nonlinearity with Disorder: Proceedings of the Tashkent Conference, Tashkent, Uzbekistan, October 1–7, 1990
Example text
When the nonlinearity vanishes as 'Yo - t 0, t - t 0 and F(l) - t OJ the contributions F(q) are O(e- q/ t ) and these also vanish when 'Yo - t O. It is a check on our initial choice of Hamiltonian eqn. actly and term by term the results (11), (12) by evaluating the classical partition function Z. This is the functional integral Z = ! (2). The functional integral (13) is taken over classical trajectories in the symplectic manifoldcoordinatised by II(:z:, t), ¢(:z:, t). (13), is evaluated by the transfer integral method (TIM) [1].
Phys. - JETP 46, 281 (1977)]. J. C. Newell, Proc. R. Soc. London Ser. A 361, 413 (1978). [8] Yuri S. Kivshar and Borsi A, Malomed, Rev. Mod. Phys. 61, 763 (1989). F. P. N. Islam, IEEE J. Quan. , QE-22, 157-173 (1986). [10] K. F. Mollenauer, Optics Letters 11, 1284 - 1286 (1989). J. Kaup, J. Math. Anal. Appl. 54, 849 (1976). 22 Deformation of Solitons in Random Media M. Wadati Department of Physics, Faculty of Science, University of Tokyo, Hongo 7-3-1, Bunkyo-Ku, Tokyo 113, Japan Abstract. A partial differential equation which describes nonlinear wave propagations in random media is presented.
The energy (30) and the "number of quasi-particles", (31) 40 ~ 0 '----' > ~ N -----'----' > 10 -I 10 -2 10 -J 10 -. 25 (Kivshar et al. [4]). ). These reflection coefficients were calculated in Ref. [24]) and the expressions are R(N) - ~ - 64NV Joroo where F(x,o:) dx F( ) R(E) x,o: , = 1("(2V roo 256E Jo 1)2 + 0: ]2 = cosh[(x2 U+(l'(x2 , + 0: 2 -1)] 2 r 0: dx x2F(x, 0:), = NjV. (32),(33) may be reduced to a system of two coupled integra-differential equations. , small 0:, the resulting system yields the approximate analytical dependences, T(N,E)(x) = N(x)jN(O) = E(x)jE(O) = exp(-xjAo), (36) where AO = V2(0)jp(2 is the localization length.
Nonlinearity with Disorder: Proceedings of the Tashkent Conference, Tashkent, Uzbekistan, October 1–7, 1990 by B. V. Chirikov (auth.), Professor Fatkulla Abdullaev, Dr. Alan R. Bishop, Dr. Stephanos Pnevmatikos (eds.)
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