Negative Order KdV Equation with No Solitary Traveling Waves

Rodríguez, Miguel; Li, Jing; Zhang, Qiao

doi:10.3390/math10010048

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2023

2024

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Cited by 4 publications

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“…In [22,23,24,25,26] it was investigated the Hamiltonian structure, an infinite set of conservation laws, N-soliton, quasi-periodic wave solutions for the KdV equation of negative order.…”

Section: Introductionmentioning

confidence: 99%

Integration of the Loaded Negative Order Korteweg-De Vries Equation in the Class of Periodic Functions

Urazboev,

Khasanov,

Ganjaev

2024

Int. J. of Appl. Math.

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In this paper, we consider the loaded Korteweg-de Vries equation of negative order in the class of periodic functions corresponding to the eigenvalues of the corresponding spectral problem. It is shown that the considered equation can be integrated by the method of the inverse spectral problem. The evolution of the spectral data of the Sturm-Liouville operator with a periodic potential associated with the solution of the considered equation is determined. The obtained results make it possible to apply the inverse problem method for solving the loaded Korteweg-de Vries equation of negative order in the class of periodic functions corresponding to the eigenvalues of the corresponding spectral problem.

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“…In [22,23,24,25,26] it was investigated the Hamiltonian structure, an infinite set of conservation laws, N-soliton, quasi-periodic wave solutions for the KdV equation of negative order.…”

Section: Introductionmentioning

confidence: 99%