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 Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 11, paper published in the English version journal (Mi zvmmf10873)

Papers published in the English version of the journal

Soliton solutions and conservation laws for an inhomogeneous fourth-order nonlinear Schrödinger equation

Pan Wanga, Feng-Hua Qib, Jian-Rong Yanga

a School of Management, Beijing Sport University, Information Road Haidian District, Beijing, China
b School of Information, Beijing Wuzi University, Beijing, China

Abstract: In this paper, we investigate an inhomogeneous fourth-order nonlinear Schrödinger (NLS) equation, generated by deforming the inhomogeneous Heisenberg ferromagnetic spin system through the space curve formalism and using the prolongation structure theory. Via the introduction of the auxiliary function, the bilinear form, one-soliton and two-soliton solutions for the inhomogeneous fourth-order NLS equation are obtained. Infinitely many conservation laws for the inhomogeneous fourth-order NLS equation are derived on the basis of the Ablowitz–Kaup–Newell–Segur system. Propagation and interactions of solitons are investigated analytically and graphically. The effect of the parameters $\mu_1$, $\mu_2$, $\nu_1$ and $\nu_2$ on the soliton velocity are presented. Through the asymptotic analysis, we have proved that the interaction of two solitons is not elastic.

Key words: inhomogeneous generalized fourth-order nonlinear Schrödinger, equation infinitely many conversation laws, auxiliary function, Hirota method, symbolic computation.

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English version:
Computational Mathematics and Mathematical Physics, 2018, 58:11, 1856–1864

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Citation: Pan Wang, Feng-Hua Qi, Jian-Rong Yang, “Soliton solutions and conservation laws for an inhomogeneous fourth-order nonlinear Schrödinger equation”, Comput. Math. Math. Phys., 58:11 (2018), 1856–1864

Citation in format AMSBIB
\Bibitem{WanQiYan18} \by Pan~Wang, Feng-Hua~Qi, Jian-Rong~Yang \paper Soliton solutions and conservation laws for an inhomogeneous fourth-order nonlinear Schrödinger equation \jour Comput. Math. Math. Phys. \yr 2018 \vol 58 \issue 11 \pages 1856--1864 \mathnet{http://mi.mathnet.ru/zvmmf10873} \crossref{https://doi.org/10.1134/S0965542518110106} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000452301900014} \elib{https://elibrary.ru/item.asp?id=38893575} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85058858611}