Results 21 to 30 of about 1,094 (76)
On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation [PDF]
, 2006 Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled by an angle $\theta$ are constructed and then reduced to the two-component Camassa--Holm model.
Aratyn, H. +2 more
core +3 more sources
Nonanalytic solutions of the KdV equation
Abstract and Applied Analysis, Volume 2004, Issue 6, Page 453-460, 2004., 2004 We construct nonanalytic solutions to the initial value problem for the KdV equation with analytic initial data in both the periodic and the nonperiodic cases.
Peter Byers, A. Alexandrou Himonas
wiley +1 more source
Motion of Inextensible Quaternionic Curves and Modified Korteweg-de Vries Equation
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 Many curve evolutions have been determined which are integrable in recent times. The motion of curves can be defined by certain integrable equations including the modified Korteweg-de Vries.
Eren Kemal
doaj +1 more source
Prolongation structure of the Krichever-Novikov equation [PDF]
, 2002 We completely describe Wahlquist-Estabrook prolongation structures (coverings) dependent on u, u_x, u_{xx}, u_{xxx} for the Krichever-Novikov equation u_t=u_{xxx}-3u_{xx}^2/(2u_x)+p(u)/u_x+au_x in the case when the polynomial p(u)=4u^3-g_2u-g_3 has ...
Igonin, Sergei, Martini, Ruud
core +5 more sources
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
wiley +1 more source
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
wiley +1 more source
A variety of soliton solutions for the fractional Wazwaz-Benjamin-Bona-Mahony equations
Results in Physics, 2019 In the present paper, the new three-dimensional modified Benjamin-Bona-Mahony equations recently introduced are analyzed with the introduction of the spatial and temporal fractional order derivatives using conformable fractional derivative.
Aly R. Seadawy +2 more
doaj +1 more source
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
wiley +1 more source
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
doaj +1 more source
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
doaj +1 more source