Calogero, Francesco; Payandeh, Farrin Solvable systems featuring 2 dependent variables evolving in discrete-time via 2 nonlinearly-coupled first-order recursion relations with polynomial right-hand sides. (English) Zbl 1462.37066 J. Nonlinear Math. Phys. 26, No. 2, 273-280 (2019). MSC: 37J35 70H06 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{F. Payandeh}, J. Nonlinear Math. Phys. 26, No. 2, 273--280 (2019; Zbl 1462.37066) Full Text: DOI arXiv
Bihun, Oksana; Calogero, Francesco Time-dependent polynomials with one double root, and related new solvable systems of nonlinear evolution equations. (English) Zbl 1457.37076 Qual. Theory Dyn. Syst. 18, No. 1, 153-181 (2019). MSC: 37J35 37J46 70H06 70F10 70K42 26C10 30C15 PDFBibTeX XMLCite \textit{O. Bihun} and \textit{F. Calogero}, Qual. Theory Dyn. Syst. 18, No. 1, 153--181 (2019; Zbl 1457.37076) Full Text: DOI arXiv
Calogero, F. Zeros of entire functions and related systems of infinitely many nonlinearly coupled evolution equations. (English. Russian original) Zbl 1403.30009 Theor. Math. Phys. 196, No. 2, 1111-1128 (2018); translation from Teor. Mat. Fiz. 196, No. 2, 193-214 (2018). MSC: 30D15 30C15 34G20 PDFBibTeX XMLCite \textit{F. Calogero}, Theor. Math. Phys. 196, No. 2, 1111--1128 (2018; Zbl 1403.30009); translation from Teor. Mat. Fiz. 196, No. 2, 193--214 (2018) Full Text: DOI
Calogero, F. On a technique to identify solvable discrete-time many-body problems. (English. Russian original) Zbl 1284.82040 Theor. Math. Phys. 172, No. 2, 1052-1072 (2012); translation from Teor. Mat. Fiz. 172, No. 2, 198-223 (2012). MSC: 82C22 37K10 81V70 PDFBibTeX XMLCite \textit{F. Calogero}, Theor. Math. Phys. 172, No. 2, 1052--1072 (2012; Zbl 1284.82040); translation from Teor. Mat. Fiz. 172, No. 2, 198--223 (2012) Full Text: DOI
Calogero, F.; Euler, M.; Euler, N. New evolution PDEs with many isochronous solutions. (English) Zbl 1177.35046 J. Math. Anal. Appl. 353, No. 2, 481-488 (2009). MSC: 35C05 35G25 35B10 PDFBibTeX XMLCite \textit{F. Calogero} et al., J. Math. Anal. Appl. 353, No. 2, 481--488 (2009; Zbl 1177.35046) Full Text: DOI
Calogero, F.; Françoise, J-P; Sommacal, M. Solvable nonlinear evolution PDEs in multidimensional space involving trigonometric functions. (English) Zbl 1115.37063 J. Phys. A, Math. Theor. 40, No. 18, F363-F368 (2007). MSC: 37L05 37N05 70H06 PDFBibTeX XMLCite \textit{F. Calogero} et al., J. Phys. A, Math. Theor. 40, No. 18, F363--F368 (2007; Zbl 1115.37063) Full Text: DOI
Calogero, F.; Degasperis, A. Novel solution of the system describing the resonant interaction of three waves. (English) Zbl 1062.37064 Physica D 200, No. 3-4, 242-256 (2005). MSC: 37K10 35Q58 37K40 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{A. Degasperis}, Physica D 200, No. 3--4, 242--256 (2005; Zbl 1062.37064) Full Text: DOI
Calogero, Francesco A technique to identify solvable dynamical systems, and another solvable extension of the goldfish many-body problem. (English) Zbl 1064.70010 J. Math. Phys. 45, No. 12, 4661-4678 (2004). MSC: 70F10 70H06 PDFBibTeX XMLCite \textit{F. Calogero}, J. Math. Phys. 45, No. 12, 4661--4678 (2004; Zbl 1064.70010) Full Text: DOI
Calogero, F.; Ji, Xiaoda \(C\)-integrable nonlinear PDEs. IV. (English) Zbl 0904.35085 J. Phys. A, Math. Gen. 29, No. 21, 6781-6794 (1996). MSC: 35Q58 37J35 37K10 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{X. Ji}, J. Phys. A, Math. Gen. 29, No. 21, 6781--6794 (1996; Zbl 0904.35085) Full Text: DOI
Calogero, F. Some ideas and results on integrable nonlinear evolution systems. (English) Zbl 0749.35014 Differential geometric methods in theoretical physics, Proc. 19th Int. Conf., Rapallo/Italy 1990, Lect. Notes Phys. 375, 91-95 (1991). Reviewer: A.Klíč (Praha) MSC: 35G10 35K25 35Q58 35K55 37J35 37K10 PDFBibTeX XMLCite \textit{F. Calogero}, Lect. Notes Phys. 375, 91--95 (1991; Zbl 0749.35014)
Calogero, F. Some ideas on nonlinear evolution equations. (English) Zbl 0728.35108 Nonlinear physics, Proc. Int. Conf., Shanghai/China 1989, 232-235 (1990). MSC: 35Q53 35G10 35K25 PDFBibTeX XML
Calogero, F. Universality and integrability of the nonlinear evolution PDE’s describing N-wave interactions. (English) Zbl 0692.35100 J. Math. Phys. 30, No. 1, 28-40 (1989). MSC: 35Q99 37J35 37K10 PDFBibTeX XMLCite \textit{F. Calogero}, J. Math. Phys. 30, No. 1, 28--40 (1989; Zbl 0692.35100) Full Text: DOI
Calogero, Francesco; Eckhaus, Wiktor Nonlinear evolution equations, rescalings, model PDEs and their integrability. II. (English) Zbl 0702.35210 Inverse Probl. 4, No. 1, 11-33 (1988). MSC: 35Q35 35G10 35K25 35R30 35Q55 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{W. Eckhaus}, Inverse Probl. 4, No. 1, 11--33 (1988; Zbl 0702.35210) Full Text: DOI
Calogero, F. Nonlinear evolution PDEs that are applicable and integrable. (English) Zbl 0683.35078 Plasma theory and nonlinear and turbulent processes in physics, Proc. Int. Workshop, Kiev/USSR 1987, 3-6 (1988). Reviewer: J.H.Tian MSC: 35Q99 35J60 35G10 35K25 35J10 PDFBibTeX XML
Calogero, F.; De Lillo, S. Corrigendum: The Eckhaus PDE \(i\psi_ t+\psi_{xx}+2(| \psi |^ 2)_ x\psi +| \psi |^ 4\psi =0\). (English) Zbl 0655.35013 Inverse Probl. 4, No. 2, 571 (1988). MSC: 35G25 35Q99 35B30 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{S. De Lillo}, Inverse Probl. 4, No. 2, 571 (1988; Zbl 0655.35013) Full Text: DOI
Calogero, F. The evolution partial differential equation \(u_ t=u_{xxx}+3(u_{xx}u^ 2+3u^ 2_ xu)+3u_ xu^ 4\). (English) Zbl 0663.35006 J. Math. Phys. 28, 538-555 (1987). MSC: 35Q51 37K10 PDFBibTeX XMLCite \textit{F. Calogero}, J. Math. Phys. 28, 538--555 (1987; Zbl 0663.35006) Full Text: DOI
Calogero, Francesco; Eckhaus, Wiktor Necessary conditions for integrability of nonlinear PDEs. (English) Zbl 0645.35089 Inverse Probl. 3, L27-L32 (1987). MSC: 35Q99 35G20 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{W. Eckhaus}, Inverse Probl. 3, L27--L32 (1987; Zbl 0645.35089)
Calogero, Francesco; Eckhaus, Wiktor Nonlinear evolution equations, rescalings, model PDEs and their integrability. I. (English) Zbl 0645.35087 Inverse Probl. 3, 229-262 (1987). MSC: 35Q99 35G20 35B40 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{W. Eckhaus}, Inverse Probl. 3, 229--262 (1987; Zbl 0645.35087) Full Text: DOI
Calogero, F.; De Lillo, S. The Eckhaus PDE \(i\psi_ t+ \psi_{xx}+ 2(|\psi|^ 2)_ x\psi+ |\psi|^ 4\psi=0\). (English) Zbl 0645.35014 Inverse Probl. 3, 623-681 (1987). MSC: 35G25 35Q99 35B30 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{S. De Lillo}, Inverse Probl. 3, 623--681 (1987; Zbl 0645.35014) Full Text: DOI
Calogero, Francesco; Degasperis, Antonio Spectral transformation and solitons: tools to solve and investigate nonlinear evolution equations. (Spektral’nye preobrazovaniya i solitony. Metody resheniya i issledovaniya nelinejnykh ehvolyutsionnykh uravnenij). Transl. from the English. (Spektral’nye preobrazovaniya i solitony. Metody resheniya i issledovaniya nelinejnykh ehvolyutsionnykh uravnenij.) (Russian) Zbl 0673.35087 Moskva: Mir. 469 p. R. 4.70 (1985). MSC: 35Q99 35P25 35-02 34-02 35J10 34L99 35A30 81-02 81Uxx PDFBibTeX XMLCite \textit{F. Calogero} and \textit{A. Degasperis}, Spektral'nye preobrazovaniya i solitony. Metody resheniya i issledovaniya nelinejnykh ehvolyutsionnykh uravnenij (Russian). Transl. from the English. Moskva: Mir (1985; Zbl 0673.35087)
Calogero, F.; Degasperis, A. A modified modified Korteweg-de Vries equation. (English) Zbl 0608.35062 Inverse Probl. 1, 57-66 (1985). Reviewer: E.Malec MSC: 35Q99 35G25 35A30 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{A. Degasperis}, Inverse Probl. 1, 57--66 (1985; Zbl 0608.35062) Full Text: DOI
Calogero, F.; Degasperis, A. Elementary Bäcklund transformations, nonlinear superposition formulae and algebraic construction of solutions for the nonlinear evolution equations solvable by the Zakharov-Shabat spectral transform. (English) Zbl 0596.35009 Physica D 14, No. 1, 103-116 (1984). Reviewer: S.Tersian MSC: 35C05 35Q99 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{A. Degasperis}, Physica D 14, No. 1, 103--116 (1984; Zbl 0596.35009) Full Text: DOI
Calogero, F. Spectral transform and solitons. (English) Zbl 0538.76025 Statics and dynamics of nonlinear systems, Proc. Workshop, Erice/Italy 1983, Springer Ser. Solid-State Sci. 47, 7-17 (1983). MSC: 76B25 76B15 PDFBibTeX XML
Calogero, Francesco; Degasperis, Antonio Spectral transform and solitons: tools to solve and investigate nonlinear evolution equations. Vol. 1. (English) Zbl 0501.35072 Studies in Mathematics and its Applications, Vol. 13. Amsterdam -New York - Oxford: North-Holland Publishing Company. XV, 516 p. $ 111.50; Dfl. 240.00 (1982). MSC: 35Q99 35J10 34L99 81Uxx 35A30 35P25 81-02 35-02 34-02 PDFBibTeX XML
Calogero, F.; Degasperis, A. Reduction technique for matrix nonlinear evolution equations solvable by the spectral transform. (English) Zbl 0485.35076 J. Math. Phys. 22, 23-31 (1981). MSC: 35Q99 37J35 37K10 81Q05 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{A. Degasperis}, J. Math. Phys. 22, 23--31 (1981; Zbl 0485.35076) Full Text: DOI Link
Calogero, F. Spectral transform and nonlinear evolution equations. (English) Zbl 0407.35061 Nonlinear problems in theoretical physics, Proc. IX G.I.F.T. int. Semin., Jaca/Huesca 1978, Lect. Notes Phys. 98, 29-34 (1979). MSC: 35P05 35Q99 35R30 35G10 35K25 35A22 PDFBibTeX XML
Calogero, F. Nonlinear evolution equations solvable by the inverse spectral transform. (English) Zbl 0435.35070 Mathematical problems in theoretical physics, int. Conf., Rome 1977, Lect. Notes Phys. 80, 235-269 (1978). MSC: 35Q99 35G10 35K25 35A22 PDFBibTeX XML
Calogero, F.; Degasperis, A. Conservation laws for classes of nonlinear evolution equations solvable by the spectral transform. (English) Zbl 0406.35056 Commun. Math. Phys. 63, 155-176 (1978). MSC: 35Q99 35K55 35L65 35G20 35G10 35K25 35K35 PDFBibTeX XMLCite \textit{F. Calogero} and \textit{A. Degasperis}, Commun. Math. Phys. 63, 155--176 (1978; Zbl 0406.35056) Full Text: DOI
Calogero, F. Integrable many-body problems. (English) Zbl 0399.70022 Nonlinear equations in physics and mathematics, Proc. NATO adv. Study Inst., Istanbul 1977, 3-53 (1978). Reviewer: A. G. Ramm MSC: 70F99 81U10 93C20 35G10 35K25 70-02 81-02 PDFBibTeX XML
Calogero, F. (ed.) Nonlinear evolution equations solvable by the spectral transform. Lectures presented at the international symposium held at the Accademia dei Lincei in Rome, June 15 - 18, 1977. (English) Zbl 0383.00006 Research Notes in Mathematics. No. 26. London, San Francisco, Melbourne: Pitman. XVII, 257 p. £9.50 (1978). MSC: 00Bxx 35-06 PDFBibTeX XML