Sóng Lan Truyền và Sóng Đứng trong Các Đoản Rung Liên Kết và Nôi Đu Newton
Tóm tắt
Từ khóa
Tài liệu tham khảo
Alexander, J., Yorke, J.: Global bifurcations of periodic orbits. Am. J. Math. 100, 263–292 (1978)
Balanov, Z., Krawcewicz, W., Rybicki, S., Steinlein, H.: A short treatise on the equivariant degree theory and its applications. J. Fixed Point Theory Appl. 8, 1–74 (2010)
Bartsch, T.: Topological methods for variational problems with symmetries. Lecture Notes in Mathematics 1560. Springer (1993)
Berger, M.: Nonlinearity and Functional Analysis. Pure and Applied Mathematics, vol. 74. Academic Press, Cambridge (1977)
Chossat, P., Lewis, D., Ortega, J., Ratiu, T.: Bifurcation of relative equilibria in mechanical systems with symmetry. Adv. Appl. Math. 31, 10–45 (2003)
Fadell, E., Rabinowitz, P.: Bifurcation for odd potential operators and an alternative topological index. J. Funct. Anal. 26, 1–101 (1977)
Fiedler, B.: Global bifurcation of periodic solutions with symmetry. Lecture Notes in Mathematics 1309. Springer (1988)
García-Azpeitia, C., Ize, J.: Global bifurcation of polygonal relative equilibria for masses, vortices and dNLS oscillators. J. Differ. Equ. 251, 3202–3227 (2011)
García-Azpeitia, C., Ize, J.: Bifurcation of periodic solutions from a ring configuration of discrete nonlinear oscillators. DCDS-S 6, 975–983 (2013)
Golubitsky, M., Stewart, I.: Patterns of oscillation in coupled cell systems. In: Newton, P., Holmes, P., Weinstein, A. (eds.) Geometry, Mechanics, and Dynamics, pp. 243–286. Springer, Berlin (2002)
Golubitsky, M., Stewart, I., Schaeffer, D.G.: Singularities and groups in bifurcation theory II, vol. 51. Springer, Berlin (1986)
Guo, S., Lamb, J., Rink, B.: Branching patterns of wave trains in the FPU lattice. Nonlinearity 22, 283–299 (2009)
Ize, J., Vignoli, A.: Equivariant degree theory. De Gruyter Series in Nonlinear Analysis and Applications, vol. 8. Walter de Gruyter, Berlin (2003)
James, G.: Nonlinear waves in Newton’s cradle and the discrete p-Schrödinger equation. Math. Models Methods Appl. Sci. 21, 2335–2377 (2011)
James, G.: Periodic travelling waves and compactons in granular chains. J. Nonlinear Sci. 22, 813–848 (2012)
Montaldi, J., Roberts, R., Stewart, I.: Periodic solutions near equilibria of symmetric Hamiltonian systems. Phil. Trans. R. Soc. Lond. A 325, 237–293 (1988)
Pankov, A.: Travelling Waves and Periodic Oscillations in Fermi–Pasta–Ulam Lattices. The College of William and Mary, Williamsburg (2005)
Pelinovsky, D., Penati, T., Paleari, S.: Approximation of small-amplitude weakly coupled oscillators with discrete nonlinear Schrodinger equations (2015). arXiv:1509.06389
Rink, B.: Symmetry and resonance in periodic FPU chains. Commun. Math. Phys. 218, 665–685 (2001)
Stefanov, A., Krevekedis, P.: On the existence of solitary traveling waves for generalized Hertzian chains. J. Nonlinear Sci. 22, 327–349 (2012)
Vanderbauwhede, A.: Local bifurcation and symmetry. Research notes in mathematics volume 75. Pitman Advanced Publishing Program (1982)
van Gils, S., Valkering, T.: Hopf bifurcation and symmetry: standing and travelling waves in a circular chain. Jpn. J. Appl. Math. 3, 207–222 (1986)
