[Untitled]

Autor: V. K. Mel'nikov

Publikováno v: Theoretical and Mathematical Physics. 134:94-106

We propose a new approach for deriving nonlinear evolution equations solvable by the inverse scattering transform. The starting point of this approach is consideration of the evolution equations for the scattering data generated by solutions of an ar

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f137469297055063f4b1cd9b3e473a2c
https://doi.org/10.1023/a:1021823807922

Integrable and nonintegrable cases of the Lax equations with a source

Autor: V. K. Mel'nikov

Publikováno v: Theoretical and Mathematical Physics. 99:733-737

The Korteweg-de Vries equation with a source given as a Fourier integral over eigenfunctions of the so-called generating operator is considered. It is shown that, depending on the choice of the basis of the eigenfunctions, we have the following three

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::4fd8dab48753a13c5a5c16ff46edcb18
https://doi.org/10.1007/bf01017060

Integration of the nonlinear Schroedinger equation with a self-consistent source

Autor: V. K. Mel'nikov

Publikováno v: Comm. Math. Phys. 137, no. 2 (1991), 359-381

It is shown that the nonlinear Schroedinger equation with a self-consistent source admits investigation by the inverse scattering method for the Dirac operator. The conditions are found under which the solutions of the nonlinear Schroedinger equation

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b94d824993821758f552e386610b0aba
https://doi.org/10.1007/bf02431884

New method for deriving nonlinear integrable systems

Autor: V. K. Mel’nikov

Publikováno v: Journal of Mathematical Physics. 31:1106-1113

A new approach is proposed to derive nonlinear integrable systems. It is used to obtain several new nonlinear integrable systems. The above results are relevant to some problems of hydrodynamics, plasma physics, solid‐state physics, etc.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3afe83affc4815c688624c82076949b9
https://doi.org/10.1063/1.528790

H

Autor: V. N. Saliĭ, F. P. Vasil’ev, S. V. Matveev, A. N. Parshin, V. D. Kukin, A. B. Ivanov, M. S. Nikulin, I. A. Vinogradova, P. S. Soltan, Sh. A. Alimov, V. A. Il’in, V. I. Danilov, N. Kh. Rozov, M. V. Fedoryuk, M. K. Samarin, P. K. Suetin, A. V. Malyshev, Yu. A. Brychkov, A. P. Prudnikov, Ü. Lumiste, V. L. Popov, B. V. Khvedelidze, A. L. Onishchik, D. V. Alekseevskiĭ, V. I. Sobolev, V. V. Rumyantsev, A. S. Fedenko, L. D. Ivanov, I. G. Koshevmkova, G. E. Mints, A. L. Semenov, A. I. Shtern, A. D. Aleksandrov, B. A. Pasynkov, M. I. Voĭtsekhovskiĭ, E. K. Godunova, V. M. Tikhomirov, B. M. Bredikhin, V. B. Korotkov, B. M. Levitan, N. K. Nikol’skiĭ, B. S. Pavlov, E. V. Shikin, Yu. V. Komlenko, S. G. Tankeev, A. I. Ovseevich, L. P. Kuptsov, I. I. Volkov, V. S. Vladimirov, E. D. Solomentsev, K. M. Chirka, G. F. Laptev, A. V. Chernavskiĭ, V. K. Mel’nikov, E. B. Vinberg, V. E. Govorov, A. V. Mikhalev, L. A. Skornyakov, A. A. Mal’tsev, E. G. Sklyarenko, G. S. Chogoshvili, D. V. Anosov, D. M. Smirnov, I. P. Egorov, M. M. Postnikov, I. V. Dolgachev, A. V. Shokurov, N. N. Vil’yams, A. V. Prokhorov, A. G. Sveshnikov, G. G. Chernyĭ, V. D. Kuzhin, V. I. Bityutskov, G. V. Kuz’mina, Yu. I. Shokin, N. N. Yanenko, D. D. Sokolov, A. Kaneko, E. A. Chistova, A. A. Sapozhenko, B. A. Efimov, L. D. Kudryavtsev, S. M. Voronin, V. T. Bazylev, L. N. Sretenskiĭ, V. N. Remeslennikov, O. V. Sarmanov, I. A. Kvasnikov, B. L. Rozhdestvenskiĭ, V. M. Kopytov

Publikováno v: Encyclopaedia of Mathematics ISBN: 9780792329756

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c0fd871934bbf66b3f219570eb250ff8
https://doi.org/10.1007/978-1-4899-3793-3_1