Results 21 to 30 of about 80 (73)
Darboux transformation for classical acoustic spectral problem
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 49, Page 3123-3142, 2003., 2003 We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two by developing a Darboux (Moutard) transformation formalism for this problem. The procedure follows steps similar to those for the Schrödinger operator. However, there is no one‐to‐one correspondence between the two problems.
A. A. Yurova, A. V. Yurov, M. Rudnev
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Asymptotic stability of a Korteweg–de Vries equation with a two-dimensional center manifold
Advances in Nonlinear Analysis, 2018 Local asymptotic stability analysis is conducted for an initial-boundary-value problem of a Korteweg–de Vries equation posed on a finite interval [0,2π7/3]{[0,2\pi\sqrt{7/3}]}.
Tang Shuxia +3 more
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Results in Physics, 2017 The higher order nonlinear Schrödinger (NLS) equation describes ultra-short pluse propagation in optical fibres. By using the amplitude ansatz method, we derive the exact bright, dark and bright-dark solitary wave soliton solutions of the generalized ...
Aly R. Seadawy, Dianchen Lu
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Higher‐order KdV‐type equations and their stability
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 4, Page 215-220, 2001., 2001 We have derived solitary wave solutions of generalized KdV‐type equations of fifth order in terms of certain hyperbolic functions and investigated their stability. It has been found that the introduction of more dispersive effects increases the stability range.
E. V. Krishnan, Q. J. A. Khan
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An explicit solution of coupled viscous Burgers′ equation by the decomposition method
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 11, Page 675-680, 2001., 2001 We consider a coupled system of viscous Burgers′ equations with appropriate initial values using the decomposition method. In this method, the solution is calculated in the form of a convergent power series with easily computable components. The method does not need linearization, weak nonlinearity assumptions or perturbation theory.
Doğan Kaya
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Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 Using a similar approach as Korteweg and de Vries, [19], we obtain periodic solutions expressed in terms of the Jacobi elliptic function cn, [3], for the self-focusing and defocusing one-dimensional cubic nonlinear Schrödinger equations.
Bica Ion, Mucalica Ana
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p‐adic difference‐difference Lotka‐Volterra equation and ultra‐discrete limit
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 4, Page 251-260, 2001., 2001 We study the difference‐difference Lotka‐Volterra equations in p‐adic number space and its p‐adic valuation version. We point out that the structure of the space given by taking the ultra‐discrete limit is the same as that of the p‐adic valuation space. Since ultra‐discrete limit can be regarded as a classical limit of a quantum object, it implies that
Shigeki Matsutani
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Explicit solutions of generalized nonlinear Boussinesq equations
Journal of Applied Mathematics, Volume 1, Issue 1, Page 29-37, 2001., 2001 By considering the Adomian decomposition scheme, we solve a generalized Boussinesq equation. The method does not need linearization or weak nonlinearly assumptions. By using this scheme, the solutions are calculated in the form of a convergent power series with easily computable components.
Doğan Kaya
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Results in Physics, 2016 The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS) equation.
Chen Yue, Aly Seadawy, Dianchen Lu
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Chains of KP, semi‐infinite 1‐Toda lattice hierarchy and Kontsevich integral
Journal of Applied Mathematics, Volume 1, Issue 4, Page 175-193, 2001., 2001 There are well‐known constructions of integrable systems that are chains of infinitely many copies of the equations of the KP hierarchy “glued” together with some additional variables, for example, the modified KP hierarchy. Another interpretation of the latter, in terms of infinite matrices, is called the 1‐Toda lattice hierarchy.
L. A. Dickey
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