Novel solution of the system describing the resonant interaction of three waves

Physica D: Nonlinear Phenomena

Volumn 200, Issue 3-4, 2005, Pages 242-256

  Calogero, F ^a,b   Degasperis, A ^a,b  

^a UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^b INFN SEZIONE DI ROMA   (Italy)

Author keywords

Integrable PDEs; Solitons; Three wave interaction

Indexed keywords

FUNCTIONS; INTEGRATION; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; OSCILLATIONS; PARTIAL DIFFERENTIAL EQUATIONS; RESONANCE; TIME VARYING SYSTEMS;

COUPLING CONSTANTS; INTEGRABLE PDE; SPATIAL DISTANCES; THREE-WAVE INTERACTIONS;

SOLITONS;

EID: 12244258242     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2004.11.007     Document Type: Article

References (15)

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8. F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform associated with the multichannel Schroedinger problem, and properties of their solutions, Lett. Nuovo Cimento 15 (1976) 65-69; F. Calogero, A. Degasperis, Coupled nonlinear evolution equations solvable via the inverse spectral transform and solitons that come back: the boomeron, Lett. Nuovo Cimento 16 (1976) 425-433; F. Calogero, A. Degasperis, Bäcklund transformations, nonlinear superposition principle, multisoliton solutions and conserved quantities for the 'boomeron' nonlinear evolution equation, Lett. Nuovo Cimento 16 (1976) 434-438; F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform, II, Nuovo Cimento 39B (1977) 1-54; F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform associated to the matrix Schroedinger equation, in: R.K. Bullough, P.J. Caudrey (Eds.), Solitons, Topics in Current Physics, vol. 17, Springer, 1980, pp. 301-324; A. Degasperis, Solitons, boomerons, trappons, in: F. Calogero (Ed.), Nonlinear Evolution Equations Solvable by the Spectral Transform, Pitman, London, 1978, pp. 97-126.
9. F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform associated with the multichannel Schroedinger problem, and properties of their solutions, Lett. Nuovo Cimento 15 (1976) 65-69; F. Calogero, A. Degasperis, Coupled nonlinear evolution equations solvable via the inverse spectral transform and solitons that come back: the boomeron, Lett. Nuovo Cimento 16 (1976) 425-433; F. Calogero, A. Degasperis, Bäcklund transformations, nonlinear superposition principle, multisoliton solutions and conserved quantities for the 'boomeron' nonlinear evolution equation, Lett. Nuovo Cimento 16 (1976) 434-438; F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform, II, Nuovo Cimento 39B (1977) 1-54; F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform associated to the matrix Schroedinger equation, in: R.K. Bullough, P.J. Caudrey (Eds.), Solitons, Topics in Current Physics, vol. 17, Springer, 1980, pp. 301-324; A. Degasperis, Solitons, boomerons, trappons, in: F. Calogero (Ed.), Nonlinear Evolution Equations Solvable by the Spectral Transform, Pitman, London, 1978, pp. 97-126.
10. F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform associated with the multichannel Schroedinger problem, and properties of their solutions, Lett. Nuovo Cimento 15 (1976) 65-69; F. Calogero, A. Degasperis, Coupled nonlinear evolution equations solvable via the inverse spectral transform and solitons that come back: the boomeron, Lett. Nuovo Cimento 16 (1976) 425-433; F. Calogero, A. Degasperis, Bäcklund transformations, nonlinear superposition principle, multisoliton solutions and conserved quantities for the 'boomeron' nonlinear evolution equation, Lett. Nuovo Cimento 16 (1976) 434-438; F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform, II, Nuovo Cimento 39B (1977) 1-54; F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform associated to the matrix Schroedinger equation, in: R.K. Bullough, P.J. Caudrey (Eds.), Solitons, Topics in Current Physics, vol. 17, Springer, 1980, pp. 301-324; A. Degasperis, Solitons, boomerons, trappons, in: F. Calogero (Ed.), Nonlinear Evolution Equations Solvable by the Spectral Transform, Pitman, London, 1978, pp. 97-126.
11. F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform associated with the multichannel Schroedinger problem, and properties of their solutions, Lett. Nuovo Cimento 15 (1976) 65-69; F. Calogero, A. Degasperis, Coupled nonlinear evolution equations solvable via the inverse spectral transform and solitons that come back: the boomeron, Lett. Nuovo Cimento 16 (1976) 425-433; F. Calogero, A. Degasperis, Bäcklund transformations, nonlinear superposition principle, multisoliton solutions and conserved quantities for the 'boomeron' nonlinear evolution equation, Lett. Nuovo Cimento 16 (1976) 434-438; F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform, II, Nuovo Cimento 39B (1977) 1-54; F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform associated to the matrix Schroedinger equation, in: R.K. Bullough, P.J. Caudrey (Eds.), Solitons, Topics in Current Physics, vol. 17, Springer, 1980, pp. 301-324; A. Degasperis, Solitons, boomerons, trappons, in: F. Calogero (Ed.), Nonlinear Evolution Equations Solvable by the Spectral Transform, Pitman, London, 1978, pp. 97-126.
12. F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform associated with the multichannel Schroedinger problem, and properties of their solutions, Lett. Nuovo Cimento 15 (1976) 65-69; F. Calogero, A. Degasperis, Coupled nonlinear evolution equations solvable via the inverse spectral transform and solitons that come back: the boomeron, Lett. Nuovo Cimento 16 (1976) 425-433; F. Calogero, A. Degasperis, Bäcklund transformations, nonlinear superposition principle, multisoliton solutions and conserved quantities for the 'boomeron' nonlinear evolution equation, Lett. Nuovo Cimento 16 (1976) 434-438; F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform, II, Nuovo Cimento 39B (1977) 1-54; F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform associated to the matrix Schroedinger equation, in: R.K. Bullough, P.J. Caudrey (Eds.), Solitons, Topics in Current Physics, vol. 17, Springer, 1980, pp. 301-324; A. Degasperis, Solitons, boomerons, trappons, in: F. Calogero (Ed.), Nonlinear Evolution Equations Solvable by the Spectral Transform, Pitman, London, 1978, pp. 97-126.
13. F. Calogero, A. Degasperis, New integrable equations of nonlinear Schroedinger type, Stud. Appl. Math. 113 (2004) 91-137.
14. F. Calogero, A. Degasperis, New integrable PDEs of boomeronic type, in preparation.
15. A. Degasperis, S. Lombardo, Exact solutions of the 3-wave resonant interaction equation, in preparation.