Results 31 to 40 of about 1,242 (111)
Nonclassical Approximate Symmetries of Evolution Equations with a Small Parameter [PDF]
, 2006 We introduce a method of approximate nonclassical Lie-B\"acklund symmetries for partial differential equations with a small parameter and discuss applications of this method to finding of approximate solutions both integrable and nonintegrable equations ...
Kordyukova, Svetlana
core +4 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
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
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
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
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
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
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
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