Travelling Waves in Lattice Dynamical Systems

Mathematical Methods in the Applied Sciences

Volumn 23, Issue 14, 2000, Pages 1223-1235

  Pankov, A A ^a   Pfluger K ^b  

^a JUSTUS LIEBIG UNIVERSITY   (Germany)

^b FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Lattice systems; Travelling waves

Indexed keywords

EID: 0346483176     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/1099-1476(20000925)23:14<1223::AID-MMA162>3.0.CO;2-Y     Document Type: Article

References (21)

1. Arioli G, Chabrowski J. Periodic motions of a dynamical system consisting in an infinite lattice of particles. Dynamic Systems Appl. 1997; 6: 387-395.
2. Arioli G, Gazzola F. Existence and numerical approximation of periodic motions of an infinite lattice of particles. Z. Angew. Math. Phys. 1995; 46: 898-912.
3. Arioli G, Gazzola, F. Periodic motions of an infinite lattice of particles with nearest neighbor interaction. Nonlinear Anal. TMA 1996; 26: 1103-1114.
4. Arioli G, Gazzola F, Terracini S. Multibump periodic motions of an infinite lattice of particles. Math. Z. 1996; 223: 627-642.
5. Arioli G, Szulkin A. Periodic motions of an infinite lattice of particles: the strongly indefinite case. Preprint, Dip. Mat. Univ. Milano, 1997.
6. Berestycki H, Capuzzo-Dolcetta I, Nirenberg L. Variational methods for indefinite superlinear homogeneous elliptic problems. Non-linear Differential Equations Appl. 1995; 2: 553-572.
7. Duncan DB, Wattis J. Approximations of solitary waves on lattices using weak and variational formulations. Chaos Solitons Fractals 1992; 2: 505-518.
8. Eilbeck JC. Numerical studies of solitons on lattices. Nonlinear Coherent Structures in Physics and Biology, Lecture Notes in Physics Vol. 393, Springer: Berlin, 1991; 143-150.
9. Fermi E, Pasta J, Ulam S. Studies of nonlinear problems. Los Alamos Sci. Lab. Rept., LA-1940, 1995; Reprinted in Lect. Appl. Math. 1974; 15: 143-156.
10. Fermi E, Pasta J, Ulam S. Studies of nonlinear problems. Los Alamos Sci. Lab. Rept., LA-1940, 1995; Reprinted in Lect. Appl. Math. 1974; 15: 143-156.
11. Friesecke G, Pego RL. Solitary waves on FPU lattices, I. Nonlinearity. 1999; 12: 1601-1627.
12. Friesecke G, Wattis J. Existence theorem for solitary waves on lattices. Comm. Math. Phys. 1994; 161: 391-418.
13. Lions P-L. The concentration-compactness method in the calculus of variations. The locally compact case, I, II. Ann. Inst. H. Poincaré Anal. Non Linear 1984; 1: 109-145, 223-283.
14. Pankov A, Pflüger K. On a semilinear Schrödinger equation with periodic potential. Nonlinear Anal. TMA 1998; 33: 593-609.
15. Pankov A, Pflüger K. Periodic and solitary travelling wave solutions for the generalized Kadomtsev-Petviashvili equation. Math. Methods Appl. Sci. 1999; 22: 733-752.
16. Rabinowitz PH. Minimax methods in critical point theory with applications to differential equations. AMS Reg. Conf. Ser. Math. 1986; 65.
17. Ruf B, Srikanth PN. On periodic motions of lattices of Toda type via critical point theory. Arch. Rational Mech. Anal. 1994; 126: 369-385.
18. Smets D, Willem M. Solitary waves with prescribed speed on infinite lattices. J. Finct. Anal. 1997; 149: 266-275.
19. Toda M. Theory of Nonlinear Lattices. Springer: Berlin, 1989.
20. Valkering TP. Periodic permanent waves in an anharmonic chain with nearest neighbour interaction. J. Phys. 1978; A 11: 1885-1897.
21. Willem M. Minimax Methods. Birkhäuser: Boston, 1996.