NONLINEAR EVOLUTIONS

Transcription

1 Proceedings of the IVth Workshop on Nonlinear Evolution Equations and Dynamical Systems NONLINEAR EVOLUTIONS Balaruc-les-Bains, France June 1987 Editor Jerome J.P. Leon ' UNIVERStTATSE!r?L!OTHEK HANNGVtf? TECHNiSCME INFORMATiONSBiBLIOTHEK World Scientific Singapore New Jersey Hong Kong

2 VII C O N T E N T S SECTION 1 THE INVERSE SPECTRAL TRANSFORM 1.1 GENERAL ASPECTS The reduction of integrable evolution equations with examples The dynamical behavior of interacting soli tons Spectral transform and Backlund transformations for evolutions with singular dispersion relations A. DEGASPERIS 3 B. FUCHSSTEINER 13 J.J.P. LEON. 33 Gauge transformations and generating operators for the quadratic bundle Backlund charts for the Caudrey-Dodd-Gibbon and Kaup-Kupershmidt hierarchies Hierarchies of nonlinear integrable evolution equations with variable coefficients Extending Green's function formalism to general nonlinear equations Integrable quasi-linear systems: generalized hodograph transformation Reciprocal transformations and their applications V.S. GERDJIKOV M.I. IVANOV Y.S. VAKLEV C. ROGERS S. CARILLO D. LEVI D.G.' CACUCI R.B. PEREZ V. PROTOPOPESCU J. GIBBONS Y. KODAMA C. ROGERS NEW INTEGRABLE SYSTEMS 125 New results on the Kowalewski top: a Lax pair, generalizations and algebraic-geometric solutions A.G. REYMAN 127

3 VIII Coupled KdV equations associated with a novel M. ANTONOWICZ 145 Schrodinger spectral problem A.P. FORDY Cavitons as an integrable pondermotive system D.J. KAUP 161 A new integrable system including the oscillating D.J. KAUP 181 two-stream instability equation S. KAWAMOTO Some integrable equations associated with C. ATHORNE 191 symmetric spaces A 2x2 Zakharov-Shabat system with a quadratic JYH-HAO LEE 199 spectral parameter 1.3 TWO SPACIAL DIMENSIONS 209 The bi-hamiltonian formulations of integrable evolution equations in multidimensions On the relation between the bicomplex and the bilocal formalism for KP systems Symmetric functions and the KP hierarchy Spectral transforms and non canonical recursion operators in multidimensions Algebraic structure of integrable systems in D = 2+1 and routes towards multidimensional integrability Fredholm and other determinants and the T function for..the Kadomtsey-Petviashvili (KP) hierarchy P.M. SANTINI A.S. FOKAS F. MAGRI C. MOROSI G. TONDO J.J.C. NIMMO M. BOITI J.J.P. LEON F. PEMPINELLI F. NIJHOFF J.M. MAILLET C. POPPE Recursion and group structures of the integrable equations in 1+1 and 1+2 dimensions. Bilocal approach Soliton equations generalized to higher dimensions Lattice equations, hierarchies and hamiltonian structures The two-dimensional Toda-lattice and its recursion operators B.G. KONOPELCHENKO 323 A. CSIZMAZIA 339 G.L. WIERSMA 349 H.W. CAPEL 0. RAGNISCO 365

4 1.4 ALGEBRAIC AND GEOMETRICAL STRUCTURES 377 On BScklund transformations for nonlinear integrable systems Soliton equations and the representation theory of the semisimple Lie algebras Miura maps and bi-hamiltonian structures for integrable stationary flows Backlund transformation and Lie-B'acklund group A non-archimedean approach to prolongation theory Lie algebra and trace identity M.V. SAVELIEV 379 V.S. GERDJIKOV 383 M. ANTONOWICZ 391 A.P. FORDY N..ASANO 403 H.N. VAN ECK 415 G-Z. TU 425 D-Z. MENG SECTION 2 APPLICATIONS OF THE SOLITON THEORY 2.1 SOLITONS AND INTEGRABLE SYSTEMS IN PHYSICS 435 Classical Poisson bracket relations and quantum commutation relations for Davey-Stuartson Nonlinear evolution equation for the distribution of technologies according to efficiency levels C.L. SCHULTZ 437 M.J. ABLOWITZ D. BAR YAACOV G.M. HENKIN 449 V.M. POLTEROVICH Amplification of coherent optical pulses and "non-bound-state" solitons J.R. COX R.D. HOCHMAN 459 Higher order Korteweg-de Vries equation for interacting phonons in a one-dimensional anharmonic lattice R. CHATTERJEE 469 S.J. SMITH Geodesic congruences and inhomogeneous Heisenberg ferromagnet "" The forced Toda lattice: an integrable system Solitary waves in straits The KP equation and biperiodic water waves A. SYM W. WESSELIUS D. WYCOFF D.J. KAUP V. ARTALE D. LEVI N. SCHEFFNER J. HAMMACK H. SEGUR

5 2.2 NEARLY INTEGRABLE SYSTEMS, PERTURBATIVE AND NUMERICAL METHODS 529 Formation of instability regions from unstable states in nonlinear systems with dissipation Correlations between chaos in the perturbed Sine-Gordon equation and finite modal equations Nearly integrable systems: normal form and solitons Application of Lie methods to autonomous hamiltonian perturbations of the Korteweg- de Vries equation: second order calculation On the nonlinear Schrodinger equation as an averaging theory Structural stability of solutions to integrable nonlinear PDE's and explicit Poincare maps Numerical approach of the quintic Schrodinger equation Formation and competition of periodic patterns Chaotic dynamics in Josephson junction, simulations 3-D numerical hydrodynamics of self-gravitating gas I- Evolution of,a transient plasma V.G. KAMENSKY 531 S.V. MANAKOV M.G. FOREST 537 Y. KODAMA 559 C.R. MENYUK 571 E.R. TRACY 593 J.W. LARSON A.R. OSBORNE L. BERGAMASCO B. BIRNIR 603 P.- SMEREKA A. CLOOT 637 B.M. HERBST J.A.C. WEIDEMAN H.R. SCHOBER 647 W. ZIMMERMANN P.H. BORCHERDS 657 G.P. McCAULEY M. NAGASAWA S.M. MIYAMA 669 C. GAUTHEREAU 679 Y. STEPHAN 2.3 OTHER TOPICS: INTEGRABILITY, INVERSE PROBLEMS, ORDINARY DIFFERENTIAL EQUATIONS 693 On the Eckhaus equation F. CALOGERO 695 S. DE LILLO Contact symmetry groups and integrable systems J. VILLARROEL 701

6 XI Existence and nonexistence of global solution, soliton solution for a class of the systems of generalized Zakharov equations Nonintegrability of homogeneous Fokker Planck and electromagnetic Hamiltonians For an impedance scattering theory Multi-dimensional n > 3 inverse scattering theory Lyapunov exponents of experimental systems Equivalence classes of differential equations On certain functional equations connected with integrable many body dynamical systems GUO BOLING D. ROEKAERTS H. YOSHIDA P.C. SABATIER B. DeFACIO 0. BRANDER R. CONTE M. DUBOIS F M. MAHOMED P.G.L. LEACH M. BRUSCHI LIST OF PARTICIPANTS 794