Results 81 to 90 of about 49,111 (193)

Smooth and peaked solitons of the CH equation [PDF]

Journal of Physics A: Mathematical and Theoretical, 2010
The relations between smooth and peaked soliton solutions are reviewed for the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH equation in action-angle variables is expressed for solitons by using the scattering data for its associated isospectral eigenvalue problem, rephrased as a
Holm, Darryl D., Ivanov, Rossen I.
openaire   +2 more sources

Separation of variables for soliton equations via their binary constrained flows

, 1999
Binary constrained flows of soliton equations admitting $2\times 2$ Lax matrices have 2N degrees of freedom, which is twice as many as degrees of freedom in the case of mono-constrained flows.
Wen-Xiu Ma, Yunbo Zeng, Zeng Y. B.
core   +1 more source

Fractional Consistent Riccati Expansion Method and Soliton-Cnoidal Solutions for the Time-Fractional Extended Shallow Water Wave Equation in (2 + 1)-Dimension

Fractal and Fractional
In this work, a fractional consistent Riccati expansion (FCRE) method is proposed to seek soliton and soliton-cnoidal solutions for fractional nonlinear evolutional equations.
Lihua Zhang, Bo Shen, Meizhi Jia, Zhenli Wang, Gangwei Wang   +4 more
doaj   +1 more source

Algebro-Geometric Solutions of a (2+1)-Dimensional Integrable Equation Associated with the Ablowitz-Kaup-Newell-Segur Soliton Hierarchy

Advances in Mathematical Physics, 2022
The (2+1)-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known (1+1)-dimensional soliton equations associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy.
Xiaohong Chen
doaj   +1 more source

Vertex operator for the non-autonomous ultradiscrete KP equation

, 2009
We propose an ultradiscrete analogue of the vertex operator in the case of the ultradiscrete KP equation--several other ultradiscrete equations--which maps N-soliton solutions to N+1-soliton ones.Comment: 9 ...
Nagai H, Nakata Y, Shinzawa N, Tokihiro T, Yoichi Nakata   +4 more
core   +1 more source

Integrable Theory of the Perturbation Equations

, 1996
An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations: hereditary recursion operators, master symmetries, linear ...
B. Fuchssteiner, Ballantyne, Chen, Currò, David, Dorfman, Elgin, Fuchssteiner, Fuchssteiner, Fuchssteiner, Fuchssteiner, Gel'fand, Grimshaw, Herman, Karpman, Keener, Kivshar, Kodama, Kraenkel, Kraenkel, Ma, Ma, Ma, Ma, Ma, Ma, Magri, Matsuno, Oevel, Olver, Schwarz, Tamizhmani, Tanaka, W.X. Ma, Wadati, Zakharov   +35 more
core   +2 more sources

Multiple soliton solutions for the (3+1) conformable space–time fractional modified Korteweg–de-Vries equations

Journal of Ocean Engineering and Science, 2018
In the present paper, multiple exact soliton solutions for the old and the newly introduced (3+1)-dimensional modified Korteweg–de-Vries equation (mKdV) will be sought.
R.I. Nuruddeen
doaj   +1 more source

On Soliton Equations of Exceptional Type

Journal of Algebra, 1994
The explicit structure of soliton equations in bilinear form is studied. The equations studied are those corresponding to A-D-E-type Kac-Moody algebra in the basic representation \(L(\Lambda_ 0)\), with principal or homogeneous realization. Using results of Kac-Wakimoto, describing these equations with a generalized Casimir operator, the author is able
openaire   +2 more sources

Solitons from Dressing in an Algebraic Approach to the Constrained KP Hierarchy

, 1997
The algebraic matrix hierarchy approach based on affine Lie $sl (n)$ algebras leads to a variety of 1+1 soliton equations. By varying the rank of the underlying $sl (n)$ algebra as well as its gradation in the affine setting, one encompasses the set of ...
A H Zimerman, Aratyn H, Burroughs N J, Cheng Y, de Groot M F, Dickey L A, Drinfel'd V G, Drinfel'd V G, Fordy A P, Fordy A P, H Aratyn, J F Gomes, Kac V C, Kac V G, L A Ferreira, Oevel W, Wilson G, Wilson G   +17 more
core   +1 more source

On Soliton-type Solutions of Equations Associated with N-component Systems

, 2000
The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations.
Ablowitz M. J., Alber M. S., Alber M. S., Alber M. S., Alber M. S., Alonso M., Antonowicz M., Antonowicz M., Antonowicz M., Charles A. Miller, Ercolani N., Estevez P. G., Gregory G. Luther, Jaulent M., Jaulent M., Jaulent M., Khusnutdinova K. R., Mark S. Alber, Matveev V. B., Sachs R. L., Sattinger D., Sattinger D.   +21 more
core   +1 more source