# Boussinesq solitary-wave as a multiple-time solution of the Korteweg--de Vries hierarchy

## Related Articles

- On the Degree of Normalization Polynomials of the Scattering Data for Constructing Solutions of the Korteweg-de Vries Equation. Pham Loi Vu; Nguyen Huy Hoang // Southeast Asian Bulletin of Mathematics;2000, Vol. 24 Issue 4, p631
Presents a study on the solutions of the Korteweg-de Vries (KdV) equation in the class of non-scattering potentials. Results of the inverse scattering problem associated with the KdV equation on a half-line; Proof of the reduction of the normalization factors.

- Investigation of the harmonic composition of the periodic solution of the Kortewegâ€“de Vries equation. Zaıko, Yu. N. // Technical Physics Letters;Feb99, Vol. 25 Issue 2, p126
An investigation is made of the behavior of the nth harmonic of the periodic solution of the Korteweg-de Vries equation as a function of the index n in the intermediate region which is not usually investigated by soliton theory. The asymptotic forms obtained allow the harmonic behavior to be...

- Gauge and BÃ¤cklund transformations for the variable coefficient higher-order modified Kortewegâ€“de Vries equation. Zheng, Yu-kun; Chan, W. L. // Journal of Mathematical Physics;Dec88, Vol. 29 Issue 12, p2570
A family of higher-order modified Korteweg-de Vries equations with variable coefficients (t-ho-mKdV) is introduced. A one-to-one correspondence between a real solution of these equations and a complex solution of the variable coefficient higher-order Korteweg-de Vries (t-ho-KdV) equations is...

- A linearizing transformation for the Korteweg--de Vries equation; generalizations to.... // Journal of Mathematical Physics;Jul98, Vol. 39 Issue 7, p3711
Presents the transformation of the Korteweg-de Vries (KdV) equation from generalizations to higher dimensional nonlinear partial differential equations. Processes in obtaining explicit solutions of the KdV; Application of concepts to nonlinear Schrodinger equation; Discussion on the role of...

- An operator method for finding exact solutions to vector Kortewegâ€“de Vries equations. Huang, Sen-Zhong // Journal of Mathematical Physics;Mar2003, Vol. 44 Issue 3, p1357
We develop an operator method which helps finding exact solutions to nonlinear evolution equations (NLEs). Our working schema goes as follows: First we translate the given (NLE) into an appropriate operator version (ONLE). Second, we look for solutions to (ONLE) of the form U=(I+L)[sup -1]M,...

- Reflectionless Potentials and Point Interactions in Pontryagin Spaces. Kurasov, Pavel; Luger, Annemarie // Letters in Mathematical Physics;Aug2005, Vol. 73 Issue 2, p109
The problem of constructing generalized point interactions of the second derivative operator in $$L^{2}(\mathbb{R})$$ leading to the same scattering data as for reflectionless potentials is considered. It is proved that this problem has a solution only if extensions in Pontryagin spaces are...

- Reductive perturbation method of super KdV equations. Lü Ke-pu; Sun Jian-an; Duan Wen-shan; Zhao Jin-bao // Applied Mathematics & Mechanics;Jul2001, Vol. 22 Issue 7, p846
By using reductive perturbation method, super KdV equations are changed into ordinary KdV equations, small amplitude perturbation solutions are obtained.

- Characteristic Properties of the Scattering Data for the mKdV Equation on the Half-Line. Monvel, Anne Boutet de; Kotlyarov, Vladimir // Communications in Mathematical Physics;Jan2005, Vol. 253 Issue 1, p51
In this paper we describe characteristic properties of the scattering data of the compatible eigenvalue problem for the pair of differential equations related to the modified Korteweg-de Vries (mKdV) equation whose solution is defined in some half-strip or in the quarter plane...

- On the possibility of exact reciprocal transformations for one-soliton solutions to equations of the Lobachevsky class. Ratinsky, M. // Journal of Mathematical Sciences;Feb2007, Vol. 141 Issue 1, p1071
Problems on reciprocal transformation of solutions to equations of ?2-class (equations related to special coordinate nets on the Lobachevsky plane ?2) are discussed. A method of construction of solutions to one analytic differential equation of ?2-class by a given solution of another analytic...