Hirota’s bilinear method

Introduction to Hirota’s bilinear method (in conference proceedings)

• J. Hietarinta: Hirota’s bilinear method and integrability” (Bangalore, 18-29 February, 2008)
• J.Hietarinta: Introduction to the bilinear method, in “Integrability of Nonlinear Systems”, eds. Y. Kosman-Schwarzbach, B. Grammaticos and K.M. Tamizhmani, Lecture Notes in Physics Vol. 638 (Springer, 2004) pp. 95-103.
• J.Hietarinta: Bäcklund transformations from the bilinear viewpoint, CRM Proceedings and Lecture Notes 29 245-251 (2001).
• J.Hietarinta: Hirota’s bilinear method and its generalization, Int. J. Mod. Phys. A 12, 43-51 (1997).
• J.Hietarinta: Hirota’s bilinear method and partial integrability, in “Partially Integrable Equations in Physics”, eds. R. Conte and N. Boccara, (Kluwer, 1990), pp. 459-478.

Soliton solutions

• C. Gilson, J. Hietarinta, J. Nimmo and Y. Ohta: Sasa-Satsuma higher-order nonlinear Schrödinger equation
  and its bilinearization and multisoliton solutions, Phys. Rev. E 68, 016614 (2003)
• J. Hietarinta: Comment on `Exact solutions of the two-dimensional Burgers equation’, J. Phys. A:
  Math. Gen. 33 5157-5158 (2000).
• R. Radhakrishnan, M. Lakshmanan and J. Hietarinta: Inelastic collision and switching of coupled bright solitons in optical fibers, Phys. Rev. E  56, 2213-2216 (1997).
• J. Hietarinta, A. Ramani and B. Grammaticos: Continuous vacua in bilinear soliton equations, J. Phys. A:
  Math. Gen. 27, 3149-3158 (1994). 

Dromions

• J. Hietarinta: One-dromion solutions for generic classes of equations, Phys. Lett. A 149, 113-118 (1990).
• J. Hietarinta and R. Hirota: Multidromion solutions to the Davey-Stewartson equation, Phys. Lett. A 145, 237-244 (1990).
• J.Hietarinta: On the dromion masses, in “Nonlinear Evolution Equations and Dynamical Systems, Proceedings NEEDS’91”, eds. M.  Boiti, P. Martina and F. Pempinelli, (World Scientific, 1992), pp. 23-29.
• J.Hietarinta: From an analytical formula to a movie by way of REDUCE and C, in “Proceedings of the Workshop on Symbolic and Numeric Computation”, eds. H. Apiola, M. Laine and E. Valkeila, (Computing Centre, University of Helsinki, 1991) Research Reports N:o 17, pp. 117-126.
• J.Hietarinta: 2+1 Dimensional Dromions and Hirota’s Bilinear Method, in “Solitons and Chaos”, eds. I. Antoniou and F.J. Lambert, (Springer, 1991), pp. 321-324.
• J.Hietarinta: Dromion Solutions for Generic NLS- and KdV-Type Equations, in “Nonlinear Evolution Equations and Dynamical Systems, NEEDS’90”, eds. V.G. Makhankov and O.K. Pashaev, (Springer,
  1991), pp. 83-85.

The three-soliton condition as a search method

• B. Grammaticos, A. Ramani and J. Hietarinta: A search for integrable bilinear equations: the Painlevé approach, J. Math. Phys. 31, 2572-2578 (1990).
• J. Hietarinta: A search of bilinear equations passing Hirota’s three-soliton condition: IV. Complex bilinear equations, J. Math. Phys. 29, 628-635 (1988).
• J. Hietarinta: A search of bilinear equations passing Hirota’s three-soliton condition: III. sine-Gordon-type bilinear equations, J. Math. Phys. 28, 2586-2592 (1987).
• J. Hietarinta: A search of bilinear equations passing Hirota’s three-soliton condition: II. mKdV-type bilinear
  equations, J. Math. Phys. 28, 2094-2101 (1987).
• J. Hietarinta: A search of bilinear equations passing Hirota’s three-soliton condition: I. KdV-type bilinear equations, J. Math. Phys. 28, 1732-1742 (1987).
• J.Hietarinta: Searching for integrable PDE’s by testing Hirota’s three-soliton condition, in “Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation, ISSAC’91”, ed. Stephen M. Watt, (Association for Computing Machinery, 1991), pp. 295-300.
• J.Hietarinta: Equations That Pass Hirota’s Three-Soliton Condition and Other Tests of Integrability, in “Nonlinear Evolution Equations and Dynamical Systems”, eds. S. Carillo and O. Ragnisco, (Springer,
  1990), pp. 46-50.
• J.Hietarinta: Recent results from the search for bilinear equations having three-soliton solutions, in “Nonlinear evolution equations: integrability and spectral methods”, eds. A. Degasperis, A.P. Fordy and M. Lakshmanan, (Manchester U.P., 1990) pp. 307-317.

Trilinear equations

• J.Hietarinta: Gauge symmetry and the generalization of Hirota’s bilinear method, J. Nonlin. Math. Phys. 3, 260-265 (1996).
• B. Grammaticos, A. Ramani and J. Hietarinta: Multilinear operators: the natural extension of Hirota’s bilinear formalism, Phys. Lett. A 190, 65-70 (1994). 
• J. Satsuma, K. Kajiwara, J. Matsukidaira and J. Hietarinta: Solution to the Broer-Kaup system through its trilinear form, J. Phys. Soc. Jpn. 61, 3096-3102 (1992).
• J. Hietarinta and J. Satsuma: The trilinear equation as a 2+2 dimensional extension of the 1+1 dimensional relativistic Toda lattice, Phys. Lett. A 161, 267-273 (1991).
• J.Hietarinta, B. Grammaticos and A. Ramani: Integrable Trilinear PDE’s, in “Nonlinear Evolution Equations & Dynamical Systems, NEEDS ’94”, eds. V.G. Makhankov, A.R. Bishop and D.D. Holm, (World Scientific, 1995), pp. 54-63.
• J.Hietarinta, K. Kajiwara, J. Matsukidaira and J. Satsuma: The Relativistic Toda Lattice and Its Trilinear Form, in “Nonlinear Evolution Equations and Dynamical Systems, Proceedings NEEDS’91”, eds. M. Boiti, P. Martina and F. Pempinelli, (World Scientific, 1992), pp. 30-43.