Results 31 to 40 of about 2,203 (128)

Higher-Order Rogue Wave and Rational Soliton Solutions of Discrete Complex mKdV Equations

East Asian Journal on Applied Mathematics, 2018
The generalised perturbation (n, N − n)-fold Darboux transformation is used to derive new higher-order rogue wave and rational soliton solutions of the discrete complex mKdV equations.
Xiaoyong Wen
semanticscholar   +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

On the Benjamin-Bona-Mahony equation with a localized damping [PDF]

, 2016
We introduce several mechanisms to dissipate the energy in the Benjamin-Bona-Mahony (BBM) equation. We consider either a distributed (localized) feedback law, or a boundary feedback law.
Rosier, Lionel
core   +4 more sources

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
wiley   +1 more source

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
wiley   +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

Gardner's deformations of the Boussinesq equations

, 2006
Using the algebraic method of Gardner's deformations for completely integrable systems, we construct the recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri schemes for these
Karasu, Atalay, Kiselev, Arthemy V.
core   +1 more source

On Transformations of the Rabelo Equations [PDF]

, 2007
We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations.
Sakovich, Anton, Sakovich, Sergei
core   +3 more sources

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
wiley   +1 more source

Restricted Flows and the Soliton Equation with Self-Consistent Sources [PDF]

, 2006
The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Backlund transformation for the restricted flows (by V.B. Kuznetsov et al.
Lin, Runliang, Yao, Haishen, Zeng, Yunbo
core   +4 more sources