Action-angle maps and scattering theory for some finite-dimensional integrable systems. II. Solitons, antisolitons, and their bound states

Simon N. M. Ruijsenaars

Source: Publ. Res. Inst. Math. Sci. Volume 30, Number 6 (1994), 865-1008.

Related Works:

Part I: Simon Ruijsenaars. Action-angle maps and scattering theory for some finite-dimensional integrable systems. I. The pure soliton case. Comm. Math. Phys. Volume 115, Number 1 (1988), 127-165.

Project Euclid: 1104160851

Mathematical Reviews (MathSciNet): MR0929148

Zentralblatt MATH: 0667.58016

Part III: Simon Ruijsenaars. Action-angle maps and scattering theory for some finite-dimensional integrable systems. III: Sutherland type systems and their duals. Publ. Res. Inst. Math. Sci., Volume 31, Number 2 (1995), pp.247--353.

Mathematical Reviews (MathSciNet): MR1329481

Zentralblatt MATH: 0842.58050

Project Euclid: euclid.prims/1195164440

Primary Subjects: 58F07

Secondary Subjects: 35Q51, 70H05, 70H40, 81U40

Full-text: Open access

PDF File (11876 KB)

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.prims/1195164945
Mathematical Reviews number (MathSciNet): MR1322943
Zentralblatt MATH identifier: 0842.58049
Digital Object Identifier: doi:10.2977/prims/1195164945

back to Table of Contents

References

[1] Ruijsenaars, S. N. M., Action-angle maps and scattering theory for some finite-dimensional integrable systems. I. The pure soliton case, Commun. Math. Phys., 115 (1988), 127-165.

Mathematical Reviews (MathSciNet): MR929148

Zentralblatt MATH: 0667.58016

[2] Ruijsenaars, S. N. M., Relativistic Calogero-Moser systems andsolitons, In: Topics in soliton theory and exactly solvable nonlinear equations, Ablowitz, M., Fuchssteiner, B., Kruskal, M. (eds.), 182-190, World Scientific, Singapore, 1987.

Mathematical Reviews (MathSciNet): MR900392

Zentralblatt MATH: 0721.58024

[3] Ruijsenaars, S. N. M., Finite-dimensional soliton systems, In: Integrable and superintegrable systems, Kupershmidt, B. (ed.), 165-206, World Scientific, Singapore, 1990.

Mathematical Reviews (MathSciNet): MR1091264

[4] Olshanetsky, M. A., Rogov, V.-B. K., Bound states in completely integrable systems with two types of particles, Ann. Inst. H. Poincare, 29 (1978), 169-177.

Mathematical Reviews (MathSciNet): MR513688

Zentralblatt MATH: 0416.58014

[5] Olshanetsky, M. A.,Perelomov, A. M., Classical integrable finite-dimensional systems related to Lie algebras, Phys. Reps., 71 (1981), 313-400.

Mathematical Reviews (MathSciNet): MR615898

[6] Ruijsenaars, S. N. M., Schneider, H., A new class of integrable systems and its relation to solitons, Ann. Phys. (NY), 170 (1986), 370-405.

Mathematical Reviews (MathSciNet): MR851627

Zentralblatt MATH: 0608.35071

[7] Calogero, F., A sequence of Lax matrices for certain integrable Hamiltonian systems, Lett. Nuovo dm., 16 (1976), 22-24.

Mathematical Reviews (MathSciNet): MR446153

[8] Nicolaenko, B., Foias, C., Temam, R. (eds.), The connection between infinite dimensional and finite dimensional dynamical systems, Contemp. Math. 99, Amer. Math. Soc., Providence, 1987.

Mathematical Reviews (MathSciNet): MR1034490

Zentralblatt MATH: 0723.58035

[9] Tanaka, S., On the N-tuple wave solutions of the Korteweg-de Vries equation, Publ. RIMS, Kyoto Univ., 8 (1972/73), 419-427.

Mathematical Reviews (MathSciNet): MR328386

Zentralblatt MATH: 0263.35082

[10] Ohmiya, M., On the generalized soliton solutions of the modified Korteweg-de Vries equation, Osaka J. Math., 11 (1974), 61-71.

Mathematical Reviews (MathSciNet): MR352742

Zentralblatt MATH: 0282.35023

[11] Ablowitz, M. J., Segur, H., Solitons and the Inverse Scattering Transform, SIAM Stud. Appl. Math., 4, SIAM, Philadelphia, 1981.

Mathematical Reviews (MathSciNet): MR642018

Zentralblatt MATH: 0472.35002

[12] Faddeev,L. D., Takhtajan, L. A., Hamiltonian methods in the theory of solitons, Springer, Berlin, Heidelberg, New York, 1987.

Mathematical Reviews (MathSciNet): MR905674

Zentralblatt MATH: 1111.37001

[13] Poppe, C., Multipole solutions of the sine-Gordon equation, Heidelberg preprint, 1980.

[14] Tanaka, S., Non-linear Schrodinger equation and modified Korteweg-de Vries equation; construction of solutions in terms of scatering data, Publ. RIMS, Kyoto Univ., 10 (1975), 329-357.

Mathematical Reviews (MathSciNet): MR499846

Zentralblatt MATH: 0372.35069

[15] Wadati, M., Ohkuma, K., Multiple-pole solutions of the modified Korteweg-de Vries equation, J. Phys. Soc. Japan, 51 (1982), 2029-2035.

Mathematical Reviews (MathSciNet): MR669118

[16] Blaszak, M, On interacting solitons, Acta Phys. Polonica, A74 (1988), 439-444.

Mathematical Reviews (MathSciNet): MR976916

[17] Pogrebkov, A. K., Polivanov, M. K., The Liouville and sinh-Gordon equations. Singular solutions, dynamics of singularities and the inverse problem method, Sov. Sci. Rev. C Math. Phys, 5 (1985), 197-272.

Mathematical Reviews (MathSciNet): MR852218

Zentralblatt MATH: 0604.70032

[18] Guillemin, V., Sternberg, S., Symplectic techniques in physics, Cambridge University Press, Cambridge, 1984.

Mathematical Reviews (MathSciNet): MR770935

Zentralblatt MATH: 0576.58012

[19] Abraham, R., Marsden, I. E., Foundations of mechanics, Reading, Mass., Benjamin/Cummings, 1978.

Mathematical Reviews (MathSciNet): MR515141

Zentralblatt MATH: 0393.70001

[20] Pogrebkov, A. K., Private communication.

[21] Gohberg, I., Lancaster, P., Rodman, L., Matrices and indefinite scalar products, Operator theory: advances and applications, 8, Birkhauser, Basel, 1983.

Mathematical Reviews (MathSciNet): MR859708

Zentralblatt MATH: 0513.15006

[22] Ruijsenaars, S. N. M., Action-angle maps and scattering theory for some finite-dimensional integrable systems. III. Sutherland type systems and their duals, to appear in Publ. RIMS. Kyoto Univ., 31 (1995), no.2.

Mathematical Reviews (MathSciNet): MR1329481

Zentralblatt MATH: 0842.58050

previous :: next