Superposition in nonlinear wave and evolution equations

International Journal of Theoretical Physics

Volumn 45, Issue 6, 2006, Pages 1093-1109

  Schurmann H W ^a   Serov, V S ^b   Nickel, J ^a  

^a UNIVERSITY OF OSNABRÜCK   (Germany)

^b UNIVERSITY OF OULU   (Finland)

Author keywords

Linear superposition; Solitary wave solution

Indexed keywords

EID: 33745746952     PISSN: 00207748     EISSN: 15729575     Source Type: Journal    
DOI: 10.1007/s10773-006-9100-9     Document Type: Article

References (17)

1. Abramowitz, M. and Stegun, I. A. (1972). Handbook of Mathematical Functions, 9th ed., New York, Dover Publications, pp. 651-652.
2. Baldwin, D. et al. (2004). Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. J. Symb. Comp. 37, 669-705.
3. Bronstein, I. N. et al. (2000). Taschenbuch der Mathematik 5th ed., Thun und Frankfurt am Main, Verlag Harri Deutsch, pp. 40-41.
4. Chandrasekharan, K. (1985). Elliptic Functions, Berlin, Springer, p. 44.
5. Cooper, F. et al. (2002). Periodic solutions of nonlinear equations obtained by linear superposition. J. Phys. A: Math. Gen. 35, 10085-10100.
6. Drazin. P. G. (1983). Solitons, Cambridge, Cambridge University Press, p. 15.
7. Hereman, W. et al. (1986). Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method. J. Phys. A: Math. Gen. 19, 607-628.
8. Jaworski, M. and Lakshmanan, M. (2003). Comment on "Linear superposition in nonlinear equations." Phys. Rev. Lett. 90, 239401-1.
9. Khare, A. and Sukhatme, U. (2002). Cyclic identities involving Jacobi elliptic functions. J. Math. Phys. 43, 3798-3806.
10. Khare, A. and Sukhatme, U. (2002). Linear superposition in nonlinear equations. Phys. Rev. Lett. 88, 244101-1-244101-4.
11. Khare, A. et al. (2003). Cyclic identities for Jacobi elliptic and related functions. J. Math. Phys. 44, 1822-1841.
12. Schürmann, H. W. (1996). Traveling-wave solutions of the cubic-quintic Schrödinger equation. Phys. Rev. E 54, 4312-4320.
13. Schürmann, H. W. and Serov, V. S. (2004). Traveling wave solutions of a generalized modified Kadomtsev-Petviashvili equation. J. Math. Phys. 45, 2181-2817.
14. Schürmann, H. W. and Serov, V. S. (2004). Weierstrass' solutions to certain nonlinear wave and evolution equations. Proc. Progress in Electromagnetics Research Symposium March 28-31 (Pisa), pp. 651-654.
15. Wadati, M. et al. (1992). A new hamiltonian amplitude equation governing modulated wave instabilities. J. Phys. Soc. Jpn. 61, 1187-1193.
16. Weierstrass, K. (1915). Mathematische Werke V, New York, Johnson, pp. 4-16,
17. Whittaker, E. T. and Watson, G. N. (1927) A Course of Modern Analysis, Cambridge, Cambridge University Press, p. 454.