Linear superposition principle applying to Hirota bilinear equations

Computers and Mathematics with Applications

Volumn 61, Issue 4, 2011, Pages 950-959

  Ma, Wen Xiu ^a   Fan, Engui ^b  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

^b FUDAN UNIVERSITY   (China)

Author keywords

Hirota's bilinear form; N wave solution; Soliton equations

Indexed keywords

BILINEAR EQUATIONS; BILINEAR FORM; ILLUSTRATIVE EXAMPLES; LINEAR COMBINATIONS; LINEAR SUPERPOSITIONS; N-SOLITON SOLUTIONS; N-WAVE SOLUTION; SOLITON EQUATIONS; TRAVELING WAVE; WAVE SOLUTION;

MECHANICS; SOLITONS;

WAVE EQUATIONS;

EID: 79651474215     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.12.043     Document Type: Article

References (23)

1. W.X. Ma Diversity of exact solutions to a restricted BoitiLeonPempinelli dispersive long-wave system Phys. Lett. A 319 2003 325 333
2. H.C. Hu, B. Tong, and S.Y. Lou Nonsingular positon and complexiton solutions for the coupled KdV system Phys. Lett. A 351 2006 403 412
3. R. Hirota The Direct Method in Soliton Theory 2004 Cambridge University Press
4. A.P. Fordy Soliton Theory: A Survey of Results. Nonlinear Science: Theory and Applications 1990 Manchester University Press Manchester
5. J. Hietarinta Hirota's bilinear method and soliton solutions Phys. AUC 15 part 1 2005 31 37
6. W.X. Ma, and W. Srampp Bilinear forms and Bcklund transformations of the perturbation systems Phys. Lett. A 341 2005 441 449
7. W.X. Ma Integrability A. Scott, Encyclopedia of Nonlinear Science 2005 Taylor & Francis New York 450 453
8. M.J. Ablowitz, and H. Segur On the evolution of packets of water waves J. Fuid Mech. 92 1979 691 715
9. E. Infeld, and G. Rowlands Three-dimensional stability of Kortewegde Vries waves and solitons II Acta Phys. Polon. A 56 1979 329 332
10. M. Jimbo, and T. Miwa Solitons and infinite dimensional Lie algebras Publ. Res. Inst. Math. Sci. 19 1983 943 1001
11. E. Date, M. Jimbo, M. Kashiwara, and T. Miwa Transformation groups for soliton equations VIKP hierarchies of orthogonal and symplectic type J. Phys. Soc. Japan 50 1981 3813 3818
12. E. Date, M. Jimbo, M. Kashiwara, and T. Miwa Transformation groups for soliton equations IVa new hierarchy of soliton equations of KP-type Physica D 4 1981/1982 343 365
13. W.X. Ma, R.G. Zhou, and L. Gao Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in (2+1) dimensions Modern Phys. Lett. A 21 2009 1677 1688
14. E.G. Fan Quasi-periodic waves and an asymptotic property for the asymmetrical NizhnikNovikovVeselov equation J. Phys. A: Math. Theor. 42 2009 095206
15. E.G. Fan Supersymmetric KdVSawadaKoteraRamani equation and its quasi-periodic wave solutions Phys. Lett. A 374 2010 744 749
16. R. Hirota, Y. Ohta, and J. Satsuma Wronskian structures of solutions for soliton equations Recent Developments in Soliton Theory Progr. Theoret. Phys. Suppl. 94 1988 59 72
17. W.X. Ma, and Y. You Solving the Kortewegde Vries equation by its bilinear form: Wronskian solutions Trans. Amer. Math. Soc. 357 2005 1753 1778
18. X.B. Hu, and J.X. Zhao Commutativity of Pfaffianization and Bcklund transformations: the KP equation Inverse Problems 21 2005 1461 1472
19. B. Konopelchenko, and W. Strampp The AKNS hierarchy as symmetry constraint of the KP hierarchy Inverse Problems 7 1991 L17 L24
20. R.L. Lin, Y.B. Zeng, and W.X. Ma Solving the KdV hierarchy with self-consistent sources by inverse scattering method Physica A 291 2001 287 298
21. X.J. Liu, Y.B. Zeng, and R.L. Lin A new extended KP hierarchy Phys. Lett. A 372 2008 3819 3823
22. W.X. Ma An extended Harry Dym hierarchy J. Phys. A: Math. Theor. 43 2010 165202
23. W.X. Ma Commutativity of the extended KP flows Commun. Nonlinear Sci. Numer. Simul. 16 2011 722 730