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Solution by the spectral-transform method of a nonlinear evolution equation including as a special case the cylindrical KdV equation

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Lettere al Nuovo Cimento (1971-1985)

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References

  1. F. Galogero andA. Degasperis:Lett. Nuovo Cimento,23, 143 (1978). This paper is hereafter referred to as I and its notation is used here without defining it anew.

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  2. Set \( ^1 ,\psi _2 = \phi ,\varphi = \int\limits_{ - 8}^{ + 8} {dx^1 g\left( {x^1 } \right)} ,x_0 = + \infty ,x_1 = - \infty ,x_2 = + \infty \) in eq. (2.13) of the paper byF. Calogero: inStudies in Mathematical Physics, edited by E. H. Lieb, B. Simon and A. S. Wightman (Princeton, N. J., 1976)

  3. F. Calogero andA. Degasperis:Lett. Nuovo Cimento,22, 263 (1978).

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  4. F. Calogero andA. Degasperis:Lett. Nuovo Cimento,22, 270 (1978).

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  5. S. Maxon andJ. Viecelli:Phys. Fluids,17, 1614 (1974); S. Maxon:Phys. Fluids,19, 266 (1976), and preprint UCRL-78341 (to appear in theRocky Mountain Mathematics Journal, Proceedings of the Tucson Conference on Solitons (1976)); P. V. Panat:Phys. Fluids,19, 915 (1976); S. G. Tagore and P. K. Shukla:Phys. Fluids,20, 868 (1977); M. Hershkowitz and T. Romesser:Phys. Rev. Lett.,32, 581 (1974). The connection of this equation to the Schrödinger spectral problem with an additional term linear inx was first noted by V. S. Dryuma:Isv. Akad. Nauk. Mold. SSR,3, 87 (1976) (in Russian).

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  6. An explicit (but singular) solution, also involving theAi function, of (21) was already found by V. S. Dryuma (result presented at theJadwisin Soliton Meeting, Poland, September, 1977; to be published).

  7. F. Calogero andA. Degasperis:Lett. Nuovo Cimento,23, 155 (1978).

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Authors and Affiliations

  1. Istituto di Fisica dell’ Università, 00185, Roma

    F. Calogero & A. Degasperis

  2. Sezione di Roma, Istituto Nazionale di Fisica Nueleare, Italy

    F. Calogero & A. Degasperis

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  1. F. Calogero
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  2. A. Degasperis
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Calogero, F., Degasperis, A. Solution by the spectral-transform method of a nonlinear evolution equation including as a special case the cylindrical KdV equation. Lett. Nuovo Cimento 23, 150–154 (1978). https://doi.org/10.1007/BF02763081

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