Results 31 to 40 of about 1,252 (111)
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
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
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
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
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
Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain
Journal of Partial Differential Equations, 2018 In this paper, we study exact controllability and feedback stabilization for the distributed parameter control system described by high-order KdV equation posed on a periodic domain T with an internal control acting on an arbitrary small nonempty ...
Z. Meng
semanticscholar +1 more source
Riemann-Hilbert Approach and N-Soliton Solutions For Three-Component Coupled Hirota Equations
East Asian Journal on Applied Mathematics, 2020 A Riemann-Hilbert problem is employed to study integrable three-component coupled Hirota (tcCH) equations. Thus, we investigate the spectral properties of tcCH equations with a 4× 4 Lax pair and derive a Riemann-Hilbert problem, the solution of which is ...
Xin Wu, Shou-Fu Tian, Jin-Jie Yang
semanticscholar +1 more source
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