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Nonlinear physics: theory and experiment II. Proceedings of the workshop, Gallipoli, Italy, June 27 – July 6, 2002. (English) Zbl 1051.81500

River Edge, NJ: World Scientific (ISBN 981-238-270-4). xvi, 421 p. (2003).

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Publisher’s description: The theory of solitons involves a broad variety of mathematical methods and appears in many areas of physics, technology, biology, and pure and applied mathematics. In this book, emphasis is placed on both theory (considering mathematical approaches for classical and quantum nonlinear systems, both continuous and discrete) and experiment (with special discussions on high bit rate optical communications and pulse dynamics in optical materials).
For Vol. I, see E. Alfinito et al. (ed.), Lecce 1995, World Scientific (1996; Zbl 0941.00008). Contents: M. J. Ablowitz, B. Prinari and A. D. Trubatch, On the IST for discrete nonlinear Schrödinger systems and polarization shift for discrete vector solitons (3–16); T. Alagesan, Soliton solutions of coupled nonlinear Klein-Gordon equations (17–22); G. A. Alekseev, Characteristic initial value problems for integrable hyperbolic reductions of Einstein’s equations (23–29); M. Boiti, F. Pempinelli, B. Prinari and A. Spire, Discrete sine-Gordon equation (30–36); A. Degasperis, D. D. Holm and A. N. W. Hone, Integrable and non-integrable equations with peakons (37–43); S. De Lillo, M. C. Salvatori and G. Sanchini, Solution of a free boundary problem for a nonlinear diffusion-convection equation (44–50); P. G. Estevez, Iterative construction of solutions for a nonisospectral problem in \((2+1)\) dimensions (51–56); S. Flach, J. Dorignac, A. E. Miroshnichenko and V. Fleurov, Discrete breathers close to the anticontinuum limit: existence and wave scattering (57–63); V. S. Gerdjikov, Complex Toda chain – an integrable universal model for adiabatic \(N\)-soliton interactions! (64–70); Georgi G. Grahovski, On the reductions and scattering data for the generalized Zakharov-Shabat systems (71–78); Jyh-Hao Lee and Oktay K. Pashaev, Bilinear representation for the modified nonlinear Schrödinger equations and their quantum potential deformations (79–82); L. Martina and O. K. Pashaev, Noncommutative Burgers’ equation (83–88); Boris Konopelchenko and Antonio Moro, On the quasi-classical \(\overline\partial\)-dressing method (89–93);
A. Yu. Orlov, New solvable matrix integrals – \(U(n)\) case (94–100); Maxim V. Pavlov, Integrable hydrodynamic chains (101–107); A. K. Pogrebkov, KPII: new results and open problems (108–117); P. C. Sabatier, A workmate for KdV (118–124); A. Spire, V. V. Konotop and L. Vazquez, Space-time lattice for operator Schrödinger equation (125–131); Derchyi Wu, On isomonodromy deformations for the ZS-AKNS flows (132–139); M. S. Bruzón, M. L. Gandarias, E. Medina and C. Muriel, New symmetry reductions for a lubrication model (143–148); R. K. Bullough and Miki Wadati, Quantum solitons for quantum information and quantum computing (149–159); A. Cafarella, C. Corianò and M. Guzzi, Solving renormalization group equations by recursion relations (160–163); L. Degiovanni and G. Magnano, A tri-Hamiltonian route to spectral curves (164–171); V. S. Gerdjikov, A. Kyuldjiev, G. Marmo and G. Vilasi, Construction of real forms of complexified Hamiltonian dynamical systems (172–178); M. Giordano, G. Marmo, A. Simoni and F. Ventriglia, Integrable and super-integrable systems in classical and quantum mechanics (179–185); P. A. Horváthy, Non-commuting coordinates in vortex dynamics and in the Hall effect, related to “exotic” Galilean symmetry (186–192); L. S. Isaev and A. P. Protogenov, Structure of multi-meron knot action (193–199); O. I. Mokhov, Compatible nonlocal Poisson brackets of hydrodynamic type and integrable reductions of the Lamé equations (200–206); G. Scolarici, Pseudoanti-Hermiticity in QQM, time-reversal and Kramers degeneracy (207–210); P. Tempesta, R. A. Leo and G. Soliani, On the integrability of supersymmetric equations (211–217); G. De Matteis, Group analysis of the membrane shape equation (221–226); A. M. Grundland and W. J. Zakrzewski, Conformal immersions for CMC-surfaces with the same Gauss map (227–233); Yuji Kodama and Boris G. Konopelchenko, Deformations of plane algebraic curves and integrable systems of hydrodynamic type (234–240); G. Landolfi, Classical and statistical aspects of rigid surfaces systems (241–247); L. Martina, T. A. Kozhamkulov, Kur. Myrzakul and R. Myrzakulov, Integrable Heisenberg ferromagnets and soliton geometry of curves and surfaces (248–253); M. Palese and E. Winterroth, On the geometry of Bäcklund transformations (254–257); A. Aigner and V. M. Rothos, Homoclinic orbits in a near-integrable mixed type CNLS system (261–267); Marek Jaworski, A nonisospectral problem associated with the multidimensional Schrödinger equation (268–272); Kimiaki Konno and Hiroshi Kakuhata, Stretching of vortex filament with corrections (273–279); V. V. Konotop, G. L. Alfimov, P. G. Kevrekidis and M. Salerno, On the reduction of a nonlinear Schrödinger equation with a periodic potential to a vector lattice (280–286); B. Pelloni, Linear and nonlinear waves on a finite interval (287–294); C. M. Schober, Rogue waves in deep water (295–301); A. Vanossi, J. Röder, A. R. Bishop and V. Bortolani, Nonlinear dynamics of a quasiperiodic Frenkel-Kontorova model (302–308); Y. Zolotaryuk, P. L. Christiansen and M. Salerno, Ratchet-like motion of AC driven topological solitons (309–315); Mark J. Ablowitz and Ziad H. Musslimani, Discrete scalar and vector diffraction-managed nonlinear Schrödinger equation (319–332); Belal E. Baaquie, Claudio Corianò and Marakani Srikant, Quantum mechanics, path integrals and option pricing: reducing the complexity of finance (333–339); S. Boscolo, S. K. Turitsyn and K. J. Blow, Optimal dispersion maps for multichannel soliton transmission with distributed Raman amplification (340–346); Sarbarish Chakravarty and Gino Biondini, On the characteristic parameters of dispersion-managed optical pulses (351–358); T. Dobrowolski, An influence of impurities on production of kinks (359–364); R. Fedele, M. Onorato, H. Schamel, P. K. Shukla and N. L. Tsintsadze, A novel approach for determining solitary wave solutions of nonlinear Schrödinger equations (365–371); Sergio De Nicola, Renato Fedele, Margarita A. Man’ko and VladimirI. Man’ko, Wigner picture and tomographic representation of envelope solitons (372–378); R. O. Moore, G. Biondini and W. L. Kath, Importance sampling for noise-induced amplitude and timing jitter in soliton transmission systems (383–390).
The articles of this volume will be announced individually.
Indexed articles:
Ablowitz, M. J.; Prinari, B.; Trubatch, A. D., On the IST for discrete nonlinear Schrödinger systems and polarization shift for discrete vector solitons., 3-16 [Zbl 1053.37053]
Alagesan, T., Soliton solutions of coupled nonlinear Klein-Gordon equations., 17-22 [Zbl 1053.35535]
Alekseev, G. A., Characteristic initial value problems for integrable hyperbolic reductions of Einstein’s equations., 23-29 [Zbl 1053.83504]
Boiti, M.; Pempinelli, F.; Prinari, B.; Spire, A., Discrete sine-Gordon equation., 30-36 [Zbl 1053.37037]
Degasperis, A.; Holm, D. D.; Hone, A. N. W., Integrable and non-integrable equations with peakons., 37-43 [Zbl 1053.37039]
De Lillo, S.; Salvatori, M. C.; Sanchini, G., Solution of a free boundary problem for a nonlinear diffusion-convection equation., 44-50 [Zbl 1053.35549]
Estevez, P. G., Iterative construction of solutions for a nonisospectral problem in \((2+1)\) dimensions., 51-56 [Zbl 1053.37041]
Flach, S.; Dorignac, J.; Miroshnichenko, A. E.; Fleurov, V., Discrete breathers close to the anticontinuum limit: existence and wave scattering., 57-63 [Zbl 1053.39030]
Gerdjikov, V. S., Complex Toda chain—an integrable universal model for adiabatic \(N\)-soliton interactions!, 64-70 [Zbl 1053.37062]
Grahovski, Georgi G., On the reductions and scattering data for the generalized Zakharov-Shabat systems., 71-78 [Zbl 1053.37054]
Lee, Jyh-Hao; Pashaev, Oktay K., Bilinear representation for the modified nonlinear Schrödinger equations and their quantum potential deformations., 79-82 [Zbl 1053.35542]
Martina, L.; Pashaev, O. K., Noncommutative Burgers’ equation., 83-88 [Zbl 1053.81522]
Konopelchenko, Boris; Moro, Antonio, On the quasi-classical \(\overline\partial\)-dressing method., 89-93 [Zbl 1053.37055]
Orlov, A. Yu., New solvable matrix integrals – \(U(n)\) case., 94-100 [Zbl 1053.81523]
Pavlov, Maxim V., Integrable hydrodynamic chains., 101-107 [Zbl 1053.37048]
Pogrebkov, A. K., KPII: new results and open problems., 108-117 [Zbl 1053.37049]
Sabatier, P. C., A workmate for KdV., 118-124 [Zbl 1053.37050]
Spire, A.; Konotop, V. V.; Vazquez, L., Space-time lattice for operator Schrödinger equation., 125-131 [Zbl 1053.81524]
Wu, Derchyi, On isomonodromy deformations for the ZS-AKNS flows., 132-139 [Zbl 1053.37052]
Bruzón, M. S.; Gandarias, M. L.; Medina, E.; Muriel, C., New symmetry reductions for a lubrication model., 143-148 [Zbl 1053.35011]
Bullough, R. K.; Wadati, Miki, Quantum solitons for quantum information and quantum computing., 149-159 [Zbl 1053.81512]
Cafarella, A.; Corianò, C.; Guzzi, M., Solving renormalization group equations by recursion relations., 160-163 [Zbl 1053.81070]
Degiovanni, L.; Magnano, G., A tri-Hamiltonian route to spectral curves., 164-171 [Zbl 1053.37040]
Gerdjikov, V. S.; Kyuldjiev, A.; Marmo, G.; Vilasi, G., Construction of real forms of complexified Hamiltonian dynamical systems., 172-178 [Zbl 1053.37031]
Giordano, M.; Marmo, G.; Simoni, A.; Ventriglia, F., Integrable and super-integrable systems in classical and quantum mechanics., 179-185 [Zbl 1053.37042]
Horváthy, P. A., Non-commuting coordinates in vortex dynamics and in the Hall effect, related to ”exotic” Galilean symmetry., 186-192 [Zbl 1053.82526]
Isaev, L. S.; Protogenov, A. P., Structure of multi-meron knot action., 193-199 [Zbl 1053.58504]
Mokhov, O. I., Compatible nonlocal Poisson brackets of hydrodynamic type and integrable reductions of the Lamé equations., 200-206 [Zbl 1053.37047]
Scolarici, G., Pseudoanti-Hermiticity in QQM, time-reversal and Kramers degeneracy., 207-210 [Zbl 1053.81037]
Tempesta, P.; Leo, R. A.; Soliani, G., On the integrability of supersymmetric equations., 211-217 [Zbl 1053.37051]
De Matteis, G., Group analysis of the membrane shape equation., 221-226 [Zbl 1053.35502]
Grundland, A. M.; Zakrzewski, W. J., Conformal immersions for CMC-surfaces with the same Gauss map., 227-233 [Zbl 1053.53505]
Kodama, Yuji; Konopelchenko, Boris G., Deformations of plane algebraic curves and integrable systems of hydrodynamic type., 234-240 [Zbl 1053.37056]
Landolfi, G., Classical and statistical aspects of rigid surfaces systems., 241-247 [Zbl 1053.53501]
Martina, L.; Kozhamkulov, T. A.; Myrzakul, Kur.; Myrzakulov, R., Integrable Heisenberg ferromagnets and soliton geometry of curves and surfaces., 248-253 [Zbl 1053.82503]
Palese, M.; Winterroth, E., On the geometry of Bäcklund transformations., 254-257 [Zbl 1053.58506]
Aigner, A.; Rothos, V. M., Homoclinic orbits in a near-integrable mixed type CNLS system., 261-267 [Zbl 1053.37060]
Jaworski, Marek, A nonisospectral problem associated with the multidimensional Schrödinger equation., 268-272 [Zbl 1053.81514]
Konno, Kimiaki; Kakuhata, Hiroshi, Stretching of vortex filament with corrections., 273-279 [Zbl 1053.76504]
Konotop, V. V.; Alfimov, G. L.; Kevrekidis, P. G.; Salerno, M., On the reduction of a nonlinear Schrödinger equation with a periodic potential to a vector lattice., 280-286 [Zbl 1053.81515]
Pelloni, B., Linear and nonlinear waves on a finite interval., 287-294 [Zbl 1053.35543]
Schober, C. M., Rogue waves in deep water., 295-301 [Zbl 1053.76503]
Vanossi, A.; Röder, J.; Bishop, A. R.; Bortolani, V., Nonlinear dynamics of a quasiperiodic Frenkel-Kontorova model., 302-308 [Zbl 1053.82513]
Zolotaryuk, Y.; Christiansen, P. L.; Salerno, M., Ratchet-like motion of AC driven topological solitons., 309-315 [Zbl 1053.35539]
Ablowitz, Mark J.; Musslimani, Ziad H., Discrete scalar and vector diffraction-managed nonlinear Schrödinger equation., 319-332 [Zbl 1053.78503]
Baaquie, Belal E.; Corianò, Claudio; Srikant, Marakani, Quantum mechanics, path integrals and option pricing: reducing the complexity of finance., 333-339 [Zbl 1053.81533]
Boscolo, S.; Turitsyn, S. K.; Blow, K. J., Optimal dispersion maps for multichannel soliton transmission with distributed Raman amplification., 340-346 [Zbl 1053.94006]
Chakravarty, Sarbarish; Biondini, Gino, On the characteristic parameters of dispersion-managed optical pulses., 351-358 [Zbl 1053.35540]
Dobrowolski, T., An influence of impurities on production of kinks., 359-364 [Zbl 1053.82510]
Fedele, R.; Onorato, M.; Schamel, H.; Shukla, P. K.; Tsintsadze, N. L., A novel approach for determining solitary wave solutions of nonlinear Schrödinger equations., 365-371 [Zbl 1053.35541]
De Nicola, Sergio; Fedele, Renato; Man’ko, Margarita A.; Man’ko, Vladimir I., Wigner picture and tomographic representation of envelope solitons., 372-378 [Zbl 1053.94518]
Moore, R. O.; Biondini, G.; Kath, W. L., Importance sampling for noise-induced amplitude and timing jitter in soliton transmission systems., 383-390 [Zbl 1053.78506]

MSC:

81-06 Proceedings, conferences, collections, etc. pertaining to quantum theory
35-06 Proceedings, conferences, collections, etc. pertaining to partial differential equations
37-06 Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory

Citations:

Zbl 0941.00008
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