By T. Ruggeri, M. Sammartino
This publication brings jointly numerous contributions from top specialists within the box of nonlinear wave propagation. This box, which over the last 3 many years has noticeable vital breakthroughs from the theoretical viewpoint, has lately received elevated relevance as a result of advances within the know-how of fluids e.g. at microscale or nanoscale and the popularity of the most important purposes to the knowledge of organic phenomena. Nonlinear wave idea calls for using disparate techniques, together with formal and rigorous asymptotic equipment, Lie staff idea, strength equipment, numerical research, and bifurcation conception. This ebook provides a special mix within which diverse features of the speculation are enlightened and several other real-life functions are investigated. The booklet should be a important source for utilized scientists attracted to probably the most fresh advances within the concept and within the purposes of wave propagation, surprise formation, nonequilibrium thermodynamics and effort equipment.
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Additional info for Asymptotic Methods in Nonlinear Wave Phenomena: In Honor of the 65th Birthday of Antonio Greco; Palermo, Italy, 5-7 June 2006
Differential equation for X From (6), inserting into the other isocline equation yields at (E)+ xa, (g) =0 and X satisfies the second order differential equation xxxtt + (AX, - &)At, - AXtX, =0 which cannot be obtained from a Lagrangian L(Xt,X,,X). 20721 References 1. D. Lax, Ann. Math. Studies 33, 211 (1954); Comm. Pure Appl. Math. 10, 537 (1957); Selected Papers, 2 vol. (Springer-Verlag, New York, 2005). 2. D. Lax, J . Math. Phys. 5, 611 (1964). 3. G. Boillat, Nonlinear Hyperbolic Fields & Waves in: Recent Mathematical Methods in Nonlinear Wave Propagation ed.
Anal. 121, 131 (1992). 16. - J. Peng, Appl. Math. Lett. 11, 75 (1998). 17. -T. -J. Peng, Nonlinear Anal. 52,573 (2003). 18. G. Boillat and T. Z. (5), 15-A,197 (1978). 19. T. Ruggeri, Lett. Nuovo Cimento 22, 69 (1978). 20. T. Ruggeri and A. Strumia, Prog. Theor. Phys. 59, 2121 (1978). 21. G. Boillat and T. Ruggeri, Prog. Theor. Phys. 60,1928 (1978). Acknowledgments This paper was supported by MIUR PNN (Progetto di Ricerca di lnteresse Nazionale: Nonlinear Propagation and Stability in Thermodynamical Processes of Continuous Media.
The wave velocities follow from the equations (8) ( F - A1)Gv = 0 , 6~ + A ~ w= 0 . 27 It appears immediately that X = 0 is a solution (due to the reduction (8) to the first order of the differentiated system) which is incompatible with the constraints F ~+ w 6~ = 0 . Therefore p(w) and p'(w) satisfy the isocline equation (6). As an example consider the Monge-Amphre equation3 with constant coefficients H$tt Putting + 2K$tx + L$m + M + N($tt$xx $t = p , $z - $,",)= 0 . (9) = q we can write Pt + 2Kpx + Lq, + M - Np; H + Nqx =o qt - p x = 0 which is just of the form (7) with u = ( p , q ) .
Asymptotic Methods in Nonlinear Wave Phenomena: In Honor of the 65th Birthday of Antonio Greco; Palermo, Italy, 5-7 June 2006 by T. Ruggeri, M. Sammartino