N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrödinger equation”, TMF, 72:2 (1987), 183–196; Theoret. and Math. Phys., 72:2 (1987), 809

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Teoreticheskaya i Matematicheskaya Fizika, 1987, Volume 72, Number 2, Pages 183–196 (Mi tmf5321)

This article is cited in 438 scientific papers (total in 438 papers)

Exact first-order solutions of the nonlinear Schrödinger equation

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin

Full-text PDF (1429 kB) Citations (438)

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Abstract: A method of obtaining exact solutions of the nonlinear Schrödinger equation (NSE) is suggested which is based on the substitution connecting real and imaginary parts of the solution by a linear relationship with coefficients depending on time only. The method is essentially the construction of a certain system of ordinary differential equations the solutions of which determine the solutions of NSE. The solutions obtained form a three-parameter family and are expressed in terms of the Jacobi elliptic functions and the third kind incomplete elliptic integral. In general case, the solutions are periodic in spatial variable and double-periodic in time. Particular cases for which the solutions can be expressed in terms of the Jacobi functions and elementary functions are studied in detail. Possibilities of practical applications of the solutions found are pointed out.

Received: 12.03.1986

English version:
Theoretical and Mathematical Physics, 1987, Volume 72, Issue 2, Pages 809–818
DOI: https://doi.org/10.1007/BF01017105

Bibliographic databases:

Language: Russian

Citation: N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrödinger equation”, TMF, 72:2 (1987), 183–196; Theoret. and Math. Phys., 72:2 (1987), 809–818

Citation in format AMSBIB

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https://www.mathnet.ru/eng/tmf5321

https://www.mathnet.ru/eng/tmf/v72/i2/p183

This publication is cited in the following 438 articles:

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Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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